The area bounded by the curve \(y=\sin x

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Application of Integrals

Question:

The area bounded by the curve

$y=\sin x+\cos x$ and the co-ordinate axis in the first quadrant is

Options:

$\sqrt{2}-1$

$\sqrt{2}$

$\sqrt{2}+1$

$1$

Correct Answer:

$\sqrt{2}$

Explanation:

$\begin{aligned}\text{Area}&=\int_{0}^{\frac{\pi}{2}}\cos xdx+\int_{\frac{\pi}{4}}^{\frac{\pi}{2}}(\sin x-\cos x)dx\\ &=\sqrt{2}\end{aligned}$