Question

Area bounded by the curve $f\left(x\right)=\cos x$ which is bounded by the lines $x=0$ and $x=\pi$ is

• A. $4{\left(unit\right)}^2$
• B. $1{\left(unit\right)}^2$
• C. $2{\left(unit\right)}^2$
• D. $3{\left(unit\right)}^2$

Answer 1

Answer: (C)

$2{\left(unit\right)}^2$

Since the curve of $\cos x$ is negative from $x=\frac{\pi }{2}$ to $x=\pi$, we need to negate the integration of the function and then get the area.

Area $={\int }_0^{\frac{\pi }{2}}\cos x-{\int }_{\frac{\pi }{2}}^{\pi }\cos x$

Area $=[\sin x{]}_0^{\frac{\pi }{2}}-[\sin x{]}_{\frac{\pi }{2}}^{\pi }$

Area $=1-0-0+1=2(unit{)}^2$