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  4. Area bounded by f(x)= max.( sin x, cos x) ∀ 0 ≤ x ≤ (π/2) and the co-ordinate axis is equal to

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Q. Area bounded by $f(x)= max.(\sin x,\cos x) \forall \, 0 \leq x \leq \frac{\pi}{2}$ and the co-ordinate axis is equal to

Application of Integrals

Solution:

$f(x)= \cos x \forall \, 0 \leq x \leq \frac{\pi}{4}$
$= \sin x \forall \frac{\pi}{4} < x < \frac{\pi}{2}$
$\therefore $ Required area = $\int\limits_{0}^{\pi /4 } \cos \, xdx$