AP EAMCET · Maths · Definite Integration
\[
\int_0^{\pi^2 / 4}(2 \sin \sqrt{x}+\sqrt{x} \cos \sqrt{x}) d x=
\]
- A \(\frac{\pi}{2}\)
- B \(\pi\)
- C \(\frac{\pi^2}{2}\)
- D \(\pi^2\)
Answer & Solution
Correct Answer
(C) \(\frac{\pi^2}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int_0^{\pi^2 / 4} 2 \sin \sqrt{x}+\sqrt{x} \cos \sqrt{x} d x \\ & \begin{aligned} & I= 2 \int_0^{\pi^2 / 4} \sin \sqrt{x} d x+\int_0^{\pi^2 / 4} \sqrt{x} \cos \sqrt{x} d x \\ &\left.=2[x \sin \sqrt{x}]_0^{\pi^2 / 4}-2 \int_0^{\pi^2 / 4}…
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