JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f(x)=a \sin \left(\frac{\pi x}{2}\right)+b, f^{\prime}\left(\frac{1}{2}\right)=\sqrt{2}

and

\int\limits_{0}^1 f(x) d x=\frac{2 a}{\pi}

, then

View answer and explanation

Correct option: D

a=\frac{4}{\pi}, b=0

Option D (

a=\frac{{4}}{{\pi}}, b=0

) is correct. By using the given derivative and integral conditions, we can solve for the constants a and b.

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