Integrals 1-Calculus-Quiz Solution, Exercises of Calculus

Prof. Maitreya Sawhney took quiz for Calculus during class at Chennai Mathematical Institute. This is solution he provided latter. It includes: Integral, Variables, First, Order, Integrate, Trignometric, Function, Respect, Time

Typology: Exercises

2011/2012

Uploaded on 07/20/2012

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Name: Solution Registration Number: Solution
Quiz No. 6
Calculus-I Section-3
=====================================================================
Problem: Evaluate the integral
.4sin3 2
xdx
Solution:
Let
xdxI 4sin3 2
xdxI 4sin2
2
32
)2cos1sin2()8cos1(
2
32
dxx
xdxdx 8cos
2
3
1
2
3
dxxx 8.8cos
16
3
2
3
)))(sin()())(cos((.8sin
16
3
2
3/CxfdxxfxfCxx
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Name: Solution Registration Number: Solution

Quiz No. 6

Calculus-I Section-

Problem: Evaluate the integral

3 sin 4.

2

 xdx

Solution:

Let I   3 sin 4 xdx

2

I  2 sin 4 xdx 2

( 1 cos 8 ) ( 2 sin 1 cos 2 ) 2

xdx

  dx  cos 8 xdx

 x  cos 8 x. 8 dx

sin 8. ( cos( ( )) ( ) sin( ( )) ) 16

xxC f x f xdxf xC

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