JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

Let

f(x)

be a non-negative continous function such that the area bounded by the curve

y=f(x), x

-axis and the ordinates

x=\frac{\pi}{4}, x=\beta > \frac{\pi}{4}

\left(\beta \sin \beta+\frac{\pi}{4} \cos \beta+\sqrt{2} \beta\right)

. Then

f\left(\frac{\pi}{2}\right)

View answer and explanation

Correct option: B

\left(1-\frac{\pi}{4}+\sqrt{2}\right)

Option B is correct because by differentiating the given integral equation and substituting

\beta = \frac{\pi}{2}

, we can find the value of

f(\frac{\pi}{2})

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