Integral Calculus B.Sc. Mathematics(B.Sc notes)
152 videos • 1,594 views • by Doctor of Mathematics
1
Show that perimeter of the loop of the curve 9ay^2=(x-2a)(x-5a)^2
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2
Find the length of the arc of the parabola x^2=4ay from the vertex to an extremity of the latus rect
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3
Show that the whole lenght of the curve x^2(a^2-x^2)=8a^2y^2
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4
Find the length of the arc of the cardiod r=a.(1-cosθ) between the points whose vectorial angles ar
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5
Find the lenght of the arc of the curve x=e^t.sint;y=e^t.cost from t=0 to t=π/2
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6
Find the perimeter of the curve r=a.cosθ (B.Sc.Mathematics:Integral Calculus:Rectification)
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7
Show that the entire length of cardiod r=a(1+cosθ) is 8a. (Rectification in polar form:B.Sc.Maths)
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8
Find the length of the curve x^2/3+y^2/3=a^2/3 (Astroid) (Rectification)
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9
Find the length of complete cycloid
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10
Find the area enclosed by the curve y=3x-x^2; x-axis and the lines x=0 and x=3.
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11
Find the area enclosed between y^2=4ax and its latus rectum
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12
Find the area enclosed by the curve xy^2=4(2-x) and the y-axis [B.Sc. Mathematics:Quadrature]
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13
Find the area of the loop of the curve ay^2=x^2.(a-x) [B.Sc. Mathematics:Quadrature in hindi/urdu]
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14
Find the area of the loop of the curve ay^2=x^2.(a-x) [B.Sc. Mathematics:Quadrature in hindi/urdu]
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15
Find the area of the curve x=a.cos^3(t), y=b.sin^3(t) [Hypocycloid] B.Sc. Mathematics Quadrature in
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16
Find the whole area of the circle r=2a.cos2θ
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17
Find the area of the loops of the curve r=a.sin3θ.[Three leaved rose]
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18
Show that the volume of the solid generated by revolving the curve astroid x^2/3+y^2/3=a^2/3 about x
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19
Find the volume of the solid formed by the revolution of the loop of the curve y^2=x^2(a-x) about x-
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20
Find the surface area of the solid formed by the revolving a curve r=2a.cos@ about the initial line.
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21
Find the area of the surface of revolution formed by revolving the curve r=a(1+cosθ) about the init
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22
Prove that the volume of the solid generated by ellipse
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23
Show that the volume generated by the revolution of the parabola y^2=4ax lying between the vertex an
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24
Find the surface area of the solid generated by revolving the cycloid x=a(θ+sinθ);y=a(1-cosθ) about
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25
Show that area of surface of hemisphere of radius 'a' is 2πa.
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26
Hazrat Muhammad صلى الله عليه وسلم Ka Bachpan - Part 2 - Sayyad Aminul Qadri
Shemaroo Ibaadat
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27
B.Sc. 1st year most important question for integral Calculus of reduction formula
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28
B.Sc. 1st year most important question for integral Calculus of reduction formula
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29
Limit n tends to infinity Sigma r=1 to n [r^2/n^3+r^3]
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30
Limit [n!/n^n]^1/n as n tends to infinity
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31
Lt [√n/(3+4√n)^2+√n/√2(3.√2+4√n)^2+√n/√3(3.√3+4√n)^2+...+1/49n
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32
Find the limit of P={(1+1^2/n^2)(1+2^2/n)...(1+n^2/n^2)}^(1/n) as n tends to infinity
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33
Lt [1/n^2.sec^2(1/n^2)+2/n^2.sec^2(4/n^2)+3/n^2.sec^2(9/n^2)+...+1/n.sec^2(1)] as n tend to infinity
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34
Lt (sinx/x)^1/x^2 as x tends to infinity
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35
Walli's Formula for sinx.
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36
Integrate from 0 to π/2 log(1+cosα.cosx)/cosx w.r.t. x
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37
Integrate e^mx from a to b by first principle
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38
Find the volume of solid formed by revolution of ellipse x^2/a^2+y^2/b^2=1 about x-axis.
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39
part 2:Length of arc along parabola y^2=4ax from vertex to on extrimity of latus rectum part2/2
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40
part 1:Length of arc along parabola y^2=4ax from vertex to on extrimity of latus rectum part1/2
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41
Trace thw curve y^2=x.(x-1)^2 and find the area of the loop.
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42
Show that the area included between curve y^2=x^2(a+x)/(a-x) and its asymptote is 1/2(pi+4)a^2.
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43
Find the whole area of the curve r=a(1-cosθ).
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44
The loop of the curve 2ay^2=x(x-a)^2 revlved about the x-axis .Find the volume of the solid so gener
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45
Part1:Sketch the curve y^2(4-x)x^3 and find the area bounded by the curve and its asymptote.
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46
Find the length of an arc of the parabola y^2=4ax measured from the vertex to one extremity of the
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47
Show that the entire area of x^2/3+y^2/3=a^2/3 is 3/8.πa^2.
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48
Evaluate integration from 0 to infinity tan-1ax/x(1+x^2) where a greater than 1.
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49
Find the limit n tends to infinity of the series n^2/(n+1)^3+n^2/(n+2)^3+....+1/8n
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50
Integrate w.r.t x (1+x^2)/(1-x^2).√(1+x^2+x^4)
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51
Evaluate the double integral √x^2+y^2 dy dx x=0 to1 and y=0 to x
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52
Evaluate the area of the region that lies inside circle r=acosθ and outside cardioid r=a(1-cosθ)
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53
The segment of curve x=a.sin^2t,y=a.cos^2t,t is in between 0 to π/2 is revolved about y-axis,find th
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54
Evaluate Double integration of 1/√x^2+y^2+1 w.r.t. y and x with limits
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55
Double integration of 1/√x^2+y^2+1 w.r.t. y and x with limits
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56
Find the radius of curvature at the point (r,θ) on the curve θ=√r^2-a^2/a-cos-1(a/r)
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57
Show that the functions u=x+y-z,v=x-y+z,w=x^2+y^2+z^2-2yz are not independentof one another.Also fin
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58
Find the surface of the solid generated by revolving the arc of the parabola y^2=4ax bounded by its
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59
Integrate (Sin-1x)^4 with respect to x
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60
Explanation of Shab-e-miraj and Isra on basis on special theory of relativity
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61
Find the length of curve y=log[tanh(x/2) ] from x=1 to x=2.
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62
Find the length of the arc of the curve y=x(2-x) as x varies 0 to 2.
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63
Find the length of the arc of the curve x=t^2.cost, y=t^2.sint from origin to t I. e. 0 to t.
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64
Show that the functions u=x^3+x^2y+x^2z-z^2(x+y+z),v=z+x,w=x^2-z^2+xy-zy are not independent.find re
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65
The loop of curve 2ay^2=x(x-a) ^2 revolves about the straight line y=a.Find volume of the solid so
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66
x(y^2+z) p-y(x^2+z)= z(x^2-y^2)
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67
Find the length of the curve y=x^3/2 from x=0 to x=4.
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68
Evaluate integration of coshx+sinhx.sinx/1+cosx
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69
Find the area included between the curve y^2(a-x) =x^3, and it's asymptote. cissoid
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70
To prove that a.cosbx+b.sinbx/a^2+b^2=cos(bx-tan-1b/a) /squ.roota^2+b^2=
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71
Integrate e^x.(1-x/1+x) ^2dx
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72
Evaluate integration of x. e^-1ax.cosbxdx
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73
Show value of the solid by revolving area included between y^2=x^3 and x^2=y^3 about x- axis 5π/28.
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74
Find the volume of solid generated by revolution of one arc of the cycloid x=a(θ-sinθ);y=a(1-cosθ)
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75
Integration of tan-1x/(1+x)^2 with respect to x.
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76
Integrate x. e^x.sin^2x with respect to x
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77
Find the volume of the solid that result when the region enclosed by x=y^2and y=x is revolved about
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78
Integrate(2x-2) /_/x^2-2x+5 with respect to x
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79
Integrate (e^x-1) /(e^x+1) w. r. t. x
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80
∫ logx.sin-1x dx
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81
Find the volume of a solid formed by the revolution of the curve (a-x)y^2=a^2.x about it's asymptote
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82
Find area inside the circle r=asinθ and outside the cardioid r=a(1+cosθ).
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83
show that the length of the arc of the parabola y^2=4ax cut off by the line 3y=8x is a[log2+15/16].
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84
Integrate 1/(1+x) √1+3x+3x^2 w. r. t. x
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85
Integrate 1/(x^2+a^2) √x^2+b^2 w. r. t. x
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86
∫dx/x√x^+6x+109
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87
Evaluate the integral:∫x^4/(a^2+x^2)^4dx from limit 0 to a
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88
Evaluate the integral:∫sin^4θ.cos^2θdθ
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89
Evaluate the integral:∫[√(3x+2)-1/x+2]dx
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90
Find the limit as n tends to infinity of the sum n^1/2/n^3/2+n^1/2/(n+3)^3/2+n^1/2/(n+6)^3/2+..to n
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91
Determine the position and nature of the double points of the curve x^3-y^2-7x^2+4y+15x-13=0
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92
Evaluate:B(1,2)+B(2,1) (Beta function)
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93
B(m+1,n) /B(m, n)
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94
J-10:Integrate from θ=0 to θ=π/2 sin^7θ.√cosθ in term of beta function.
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95
Evaluate:B(1/2,1/2) where B is beta function
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96
Show that arc of the upper half of the curve r=a(1-cosθ) is bisected by θ=2π/3.
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97
Find the area included between the parabolae y^2=4ax and x^2=4by||Top mathematics channel on YouTube
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98
Find the whole length of the cardioid r=a(1+cosθ).||Top mathematics channel on YouTube
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99
Find the surface area generated by the curve y=as in(x/a)||Top mathematics channel on YouTube
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100
Integrate cos2θ.log(1+tanθ)
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101
The cardioid r=a(1-cosθ) revolves about the initial line, find the volume generated.
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102
Evaluate: ∫dx/(x-3)(x+1)
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103
Evaluate: ∫cos^nx.cosnxdx limit from 0 to π/2.
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104
Integral ∫sin^6xdx. part II
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105
The part of the parabola y^2=4ax cut off by its latus rectum revolves about the tangent at the verte
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106
Evaluate:gamma(1/4). gamma(3/4)
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107
Evaluate: ∫1/(1+x^2) √(1-x^2) dx
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108
Evaluate: ∫1/(1+x^3)dx
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109
Lim [1/4n^2+1+2/4n^2+2^2+3/4n^2+3^2....n/4n^2+n^2]
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110
Prove that the surface area of a sphere of radius 'a' is 4πa^2 by method of integration.
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111
Separate real and imagine parts exp(siniθ)
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112
If In=∫^nxdx from 0 to π/4, show that In+In-2=1/n-1
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113
Find area inside the circle r=asinθ and outside cardioid r=a(1-cosθ).
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114
If a function f(x)=|x| , x=/ 0 and f(x)=0, x=0.Examine for continuity at x=0.
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115
Evaluate Sigma r^2/n^3+r^3 as n tends to infinite
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116
Evaluate Sigma n^2/n^3+r^3 as n tends to infinite
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117
Find the volume of the solid generated by the revolution of an arc of the catenary y=ccosh(x/c) abou
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118
Find the whole area of the curve a^2y^2=x^3(2a-x)
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119
Relation between polar and Cartesian coordinates
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120
Evaluate ∫∫rsinθdθdr ,θ=0 to π/2;r=0 to r=acosθ
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121
Evaluate ∫ tan^nxdr,from x=0 to π/2
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122
Legendre's Duplication Formula:Γn Γ(n+1/2)=√π/2^2n-1Γ2n
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123
Relation between beta and gamma functions
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124
Complement Formula
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125
Integration of 1/(sin2x-sinx) w.r.t. x
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126
Find surface area of solid formed by revolution about axis of y of curve ay^2=x^3 from x=0 to x=4a
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127
Find the Fourier series of function x^3.
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128
Find the volume of solid obtained by revolving the area enclosed by one aarch of the cycloid x=a(+)
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129
Evaluate ∫x^3(2ax-x^2)^3/2dx
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130
Show that the volume of the solid generated by cycloid x=a(θ+sinθ),y=a(1-cosθ), about y-axis is πa^3
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131
∫Cos^n-2x.sinnxdx from x=0 to x=π/2
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132
Find the volume revolution of curve :x=acos^3t, y=bsin^3t, i.e.(x/a)^2/3+(y/b)^2/3about x-axis
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133
Prove that β(m+1,n)/β(m,n)=m/(m+n)
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134
Find the area Between the curve x(x^2+y^2)=a(x^2-y^2) and it's asymptote.
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135
Evaluate ∫∫e^-y/ydxdy from x=0 to x=♾️ (infinity) y=x to y=♾️ Change of order of integration
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136
Evaluate ∫sin^2x/(sinx+cosx)dx from x=0 to x=π/2 (Definite Integration)
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137
Find the area of the cardioid r=a(1-cosθ).
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138
Show that,in the region D:0≤x≤1,0≤y≤x^2,the following double integration ∫∫D y/x^5+1)dA =1/10log2.
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139
Show that,in the region D:1≤x≤e,0≤y≤ln(x),the following double integration ∫∫D x^3dA =3e^4+1/16.
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140
Show that the arc of the uppper half of the curve r=a(1-cosθ) is bisected at θ=2π/3.
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141
Show that the arc of the uppper half of the curve r=a(1+cosθ) is bisected at θ=π/3.
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142
Evaluate ∫∫xy(1+x+y)dxdy Double integration
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143
Find the length of the arc of the curve x=a(θ+sinθ),y=a(1-cosθ).
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144
Find the asymptotes of the curve x(x^2+y^2)=a(x^2-y^2).Also, find the area of the loop.
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145
Find whole area of ellipse x^2/2+y^2/2=1
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146
The part of the parabola y^2=4ax cut off by the latus rectum revolves about the tangent at the verte
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147
lim n→∞[1/n+n^2/(n+1)^3+n^2/(n+2)^3+...+1/8n]
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148
Evaluate ∫∫∫dxdydz from x=0 to x=2,y=0 to y=2,z=0 to z=2.
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149
Evaluate ∫∫∫xydxdydz
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150
Find L{t^2e^at} . Find the Lp transform of the t^2e^at
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151
Find Laplace transform of t^2sinat
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152
Find Laplace transform of t^2cos2t.
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