Question

The area bounded by f (x) $=x^{2}, 0 \le x \le 1, g\left(x\right)=x+2,1\le x\le2$ and x- axis is

• A. $\frac{3}{2}$
• B. $\frac{4}{3}$
• C. $\frac{8}{3}$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Required area =AreaofOAB+Area of ABC
Now, Area of OAB =$\int\limits_{0}^{1} f\left(x\right)dx+\int\limits_{1}^{2} g \left(x\right)d x$
$=\int\limits_{0}^{1} x^{2} dx +\int\limits_{1}^{2} \left(-x+2\right)d x$
$=\frac{x^{3}}{3} | _{0}^{1}+\left[\frac{-x^{2}}{2}+2x\right]_{1}^{2}$
$=\frac{1}{3}+\left[\left(\frac{-4}{2}+4\right)-\left(\frac{-1}{2}\right)+2\right]$
$=\frac{1}{3}+\left[\left(-2+4\right)-\left(\frac{3}{2}\right)\right]$
$=\frac{1}{3}+\frac{1}{2}=\frac{5}{6} \, sq\, unit$