Question

$Letf\left(x\right)=2-|x-1|andg\left(x\right)={(x-1)}^2,then$

• A. area bounded by $f\left(x\right)$ and $g\left(x\right)$ is $\frac{7}{6}$
• B. area bounded by $f\left(x\right)$ and $g\left(x\right)$ is $\frac{7}{3}$
• C. area bounded by $f\left(x\right)$$g\left(x\right)$ and $x-$ axis is $\frac{5}{3}$
• D. area bounded by $f\left(x\right)$$g\left(x\right)$ and $x-$ axis is $\frac{5}{6}$

Answer 1

The correct option is B area bounded by $f\left(x\right)$ and $g\left(x\right)$ is $\frac{7}{3}$

Area of parabola w.r.t x axis $=g\left(X\right)$

${\int }_0^2(x-1{)}^{2}dx$

$\Rightarrow$${\left[\frac{(x-1{)}^3}{3}\right]}_0^2=\frac{1}{3}+\frac{1}{2}=\frac{2}{3}$

Area of $f\left(x\right)$

$=2\times 1+\frac{1}{2}\times 2\times 1$

$\Rightarrow$ $2+1=3$

Area bounded by $f\left(x\right)$ and $g\left(x\right)$

$=3-\frac{2}{3}=\frac{7}{3}$