The area bounded by the curves $y = \cos x$ and $y = \sin x$ between the ordinates $x = 0$ and $x =\frac{3π}{2}$, is
Answer & explanation
Correct answer: option 3
Required area A is given by
$A=\int\limits_{0}^{3π/2}|\cos x - \sin x|dx$
$⇒A=\int\limits_{0}^{π/4}|\cos x - \sin x|dx+\int\limits_{π/4}^{5π/4}|\cos x - \sin x|dx+\int\limits_{5π/4}^{3π/2}|\cos x - \sin x|dx$
$⇒A=[\sin x+\cos x]_{0}^{π/4}+[-\cos x-\sin x]_{π/4}^{5π/4}+[\sin x+\cos x]_{5π/4}^{3π/2}$
$⇒A=(\sqrt{2}-1)+(\sqrt{2}+\sqrt{2})+(-1+\sqrt{2})=4\sqrt{2}-2$