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The value of int(-pi//2)^(pi//2) log""((...

The value of `int_(-pi//2)^(pi//2) log""((2-sintheta)/(2+sintheta))d theta` is

A

0

B

1

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Let `f(theta) log ((2-sin theta)/(2+sin theta))` ,
Now, ` f(-theta) = log ((2+sin theta)/(2-sin theta) ) = - log ((2-sin theta)/(2+sin theta)) = - f(theta)`
` = [ -(x^(3))/3 + x]_(0)^(1) + [ (x^(3))/3-x]_(1)^(2) `
` = - 1/3 + 1 + 8/3 - 2 - 1/3 + 1 = 2 `
` :. f(theta) ` is an odd function .
` int _(-pi//2)^(pi//2) log ((2-sin theta )/(2+sin theta)) d theta = 0`
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DEFINITE INTEGRALS-MHT CET Corner
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