Question

The area bounded by the curves $y=$ cos $x$ and $y=$ sin $x$ between the ordinates $x=0$ and $x=\frac{3\pi }{2}$ is

• A. $4\sqrt{2}+2$
• B. $4\sqrt{2}-1$
• C. $4\sqrt{2}+1$
• D. $4\sqrt{2}-2$

Answer 1

Answer: (D)

$\underset{0}{\overset{\frac{\pi }{4}}{\int }}\left(cosx-sinx\right)dx+\underset{\frac{\pi }{4}}{\overset{\frac{5\pi }{4}}{\int }}\left(sinx-cosx\right)dx+\underset{\frac{5\pi }{4}}{\overset{\frac{3\pi }{4}}{\int }}\left(cosx-sinx\right)=4\sqrt{2}-2$