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Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=...

Suppose `int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c` where C is arbitrary constant of integration.then find value of `g'(0)+g''(pi/4)`

A

sin x

B

cos x

C

tan x

D

cot x

Text Solution

Verified by Experts

The correct Answer is:
c
Let `I=int(1-7cos^(2)x)/(sin^(7)xcos^(2)x)dx`
`rArrI=int(sec^(2)x)/(sin^(7)x)dx-7int(1)/(sin^(7)x)dx`
`rArrI=int(tanx)/(sin^(7)x)-int(-7)(sinx)^(-8)cos x tanxdx-7int(1)/(sin^(7)x)dx`
`rArrI=int(tanx)/(sin^(7)x)+7int(1)/(sin^(7)x)dx-7int(1)/(sin^(7)x)dx+C`
`rArrI=int(tanx)/(sin^(7)x)+C`
Hence , f (x) = tanx.
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