The following question consist of two statements, one labelled as the 'Assertion (A)' and theo other as 'Reason (R )' . You are to examine these two statement carefully and select the answer.
Assertion (A) : `int_(0)^(pi)sin^(7)x dx = 2 int_(0)^(pi//2) sin^(7) xdx`
Reason : `sin^(7)x` is an odd function.

Options

A. Both A and R are individually true and R is the correct explanation of A
B. Both A and R are individually true and R is not the correct explanation of A
C. A is true but R is false
D. A is false but R is true

Answer

B

Explanation

`int_(0)^(pi) sin^(7) xdx = 2int_(0)^(pi//2) sin^(7) xdx`
sin x is an odd function and for an odd function
`int_(0)^(a) f(x) dx = 2int_(0)^(a//2) sin^(7) x dx`
Hence, `int_(0)^(pi)sin^(7)xdx = 2int_(0)^(pi//2) sin^(7) xdx` is true.
So , a andR both are individually true but R is not the correct explanation of A.