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  • The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 \leq x \leq is.A.root 2 sq unitsB

Q: The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 \leq x \leq\frac{\pi}{2} is.

A. \sqrt{2} sq units

B. (\sqrt{2} + 1) sq units

C. (\sqrt{2} – 1) sq unit

D. (2\sqrt{2} – 1) sq unit

Answers (1)

The questions has given, 
y-axis, y = cosx and y = sinx, 0 \leq x \leq \pi /2 \\

\begin{aligned} &\Rightarrow \sin x=\cos x\\ &\therefore x=\frac{\pi}{4}\\ &\text { Required area }\\ &=\int_{0}^{\frac{\pi}{4}}(\cos x-\sin x) d x\\ &=[\sin \mathrm{x}+\cos \mathrm{x}]_{0}^{\frac{\pi}{4}}\\ &=\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-0-1\right)\\ &=(\sqrt{2}-1) \text { sq.units } \end{aligned}

 

 

 

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