The value of the integral _-2^2 ^2x [ x ]+ 12dx (where [x] denotes the greatest integer less than or equal to x) is:

Question

Accepted Answer

Correct answer: A. (a) JEEN Main 2019 Let f (x )= sin^2x ( x )+ 12 So, f(-x)= sin^2(-x) ( -x )+ 12 ∵(-x)=-1- (x ) ⇒f(-x)= sin^2x-1- ( x )+ 12= sin^2x- 12- ( x )=-f (x ) ⇒f (x )is odd function Hence, f (x ) dx=0

$The value of the integral \int_{- 2}^{2} \frac{s i n ^{2} x}{[ \frac{x}{π} ] + \frac{1}{2}} d x (where [x] denotes the greatest integer less than or equal to x) is:$

Solution

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