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Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for a...

Let `f(x)=(1-x)^(2) sin^(2) x+x^(2)` for all `x in RR`, and let `g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt` for all `x in (1, oo)`.
Which of the following is true?

A

g is increasing on `(1, oo)`

B

g is decreasing on `(1, oo)`

C

g is increasing on (1, 2) and decreasing on `(2, oo)`

D

g is decreasing on (1, 2) and increasing on `(2, oo)`

Text Solution

Verified by Experts

The correct Answer is:
b, d
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