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  4. The area bounded by the curve y=| cos x- sin x|, 0 ≤ x ≤ (π/2) and above x-axis is

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Q. The area bounded by the curve $y=|\cos x-\sin x|, 0 \leq x \leq \frac{\pi}{2}$ and above $x$-axis is

Application of Integrals

Solution:

image
So, required area $=\int\limits_0^{\pi / 4}(\cos x-\sin x) d x+\int\limits_{\pi / 4}^{\pi / 2}-(\cos x-\sin x) d x=2(\sqrt{2}-1)$