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If intcos2018xsin^(2016)x dx=f(x)+c, whe...

If `intcos2018xsin^(2016)x dx=f(x)+c`, where `f(0)=0`, then

A

`int_(0)^(pi)f(x)dx=f(pi)`

B

`f((pi/4)=1/(2^(1009)) . 1/2017`

C

`f((pi)/4)=1/((2018)2^(1009))`

D

`f(x)` is odd function

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`:.intcos(2017x+x)sin^(2016)x dx=intcos2017 x sin^(2016)x cos x dx - int sinn 2017 x sin^(2017)x dx `……….i
`{ :' underset(I) (int cos 2017)x underset(II)ubrace(sin^(2016)xcosx) dx=(cos2017xsin^(2017)x)/2017+int(2017sin2017x)/2017 sin^(2017)xdx}`
`:.intcos2018xsin^(2017)x dx=1/2017 cos 2017 x sin^(2017)x`
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