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If I1=int0^pixf(sin^3x+cos^2x)dxa n d I...

If `I_1=int_0^pixf(sin^3x+cos^2x)dxa n d` `I_2=int_0^(pi/2)f(sin^3x+cos^2x)dx ,t h e nr e l a t eI_1a n dI_2`

Text Solution

Verified by Experts

The correct Answer is:
`I_(1)=piI_(2)`
`I_(1)=int_(0)^(1)(pi-x)f(sin^(3)x+cos^(2)x)dx`
`:. 2I=pi int_(0)^(pi)f(sin^(3)x+cos^(2)x) dx`
`=2pi int_(0)^(pi//2) f(sin^(3)x+cos^(2)x)dx`
or `I_(1)=pi int_(0)^(pi//2) f(sin^(3)x+cos^(2)x)dx=piI_(2)`
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