Question

The area bounded by the parabola $y=x^2+2,$ X - axis and lines $x=1$ and $x=2$ is _______

• A. $\frac{9}{2}$
• B. $\frac{13}{3}$
• C. $\frac{7}{3}$
• D. $\frac{32}{3}$

Answer 1

Answer: (B)

$\frac{13}{3}$

The required area is

$A={\int }_1^{2}ydx$

$⟹A={\int }_1^2(x^2+2)dx$

$⟹A={[\frac{x^3}{3}+2x]}_1^2$

$=(\frac{8}{3}+4)-(\frac{1}{3}+2)$

$⟹A=\frac{13}{3}$