Question

Find the area bounded by the curve $y=2\cos x$ and the x-axis from $x=0$ to $x=2\pi$:

• A. 18 sq. units.
• B. 12 sq. units.
• C. 8 sq. units.
• D. 4 sq. units.

Answer 1

Answer: (C)

8 sq. units.

From figure required area
$={\int }_0^{\frac{\pi }{2}}2\cos xdx-{\int }_{\frac{\pi }{2}}^{\frac{3\pi }{2}}2\cos x+{\int }_{\frac{3\pi }{2}}^{\frac{\pi }{2}}2\cos xdx$
$={\left[2\sin x\right]}_0^{\frac{\pi }{2}}-{\left[2\sin x\right]}_{\frac{\pi }{2}}^{\frac{3\pi }{2}}+{\left[2\sin x\right]}_{\frac{3\pi }{2}}^{2\pi }=8$