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Grade: 12


Find the value of the Integral -p/2 to p/2 v(cos x-cos ³x)dx

6 years ago

Answers : (2)

Sher Mohammad
IIT Delhi
askIITians Faculty
174 Points

6 years ago
Bhanutej Prabhakar Ravilla
23 Points
							taking cos x common from the term in the brackets the given integral sum is simplified to 
integral (vcosx).sinx dx
substitute cosx = t(say)
then -sinx.dx=dt
the integral again becomes :
integral(-pi/2 to pi/2) of -(vt).dt
now  we observe that the function root(cosx-cosx^3) is an even function as changing the variable x to its negative (-x) dosnt change the equation.
so integral(-pi/2 to pi/2 ) becomes:
2*integral(0 to pi/2)-(vt).dt
but wen x=0 cosx in 1. and wen x=pi/2 ,cosx is 0. so the integral again becomes:
2*integral(1 to 0) -(vt).dt
now interchange the limts of the integral and take out the negative sign.the integral now is:

2*integral(0 to one)(vt).dt   which is simply:
2*(2/3)*(t^3/2) from 0 to 1
which is -------->>>4/3.
6 years ago
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