The value of ₀^{π/2}≤ft(4+3 x/4+3 x)dx is - NCERT Class XII ...

NCERT Class XII Mathematics Chapter - - Solutions

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Choose the correct answer in Exercises 227 and 228.

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Question : 228 of 271

Marks: +1, -0

The value of

\int\limits_{0}^{\pi/2}\log\left(\frac{4+3\sin x}{4+3\cos x}\right)dx

is

2
$\frac{3}{4}$
0
–2

Solution:

Let

I=\int\limits_{0}^{\pi/2}\log\left(\frac{4+3\sin x}{4+3\cos x}\right)dx

Also,

I=\int\limits_{0}^{\pi/2}\log\left[\frac{4+3\sin(\pi/2 - x)}{4+3\cos(\pi/2 - x)}\right]dx

\Rightarrow I=\int\limits_{0}^{\pi/2}\log\left(\frac{4+3\cos x}{4+3\sin x}\right)dx

\Rightarrow I=-\int\limits_{0}^{\pi/2}\log\left(\frac{4+3\sin x}{4+3\cos x}\right)dx

\Rightarrow I=-I

\Rightarrow 2I=0\Rightarrow I=0

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