The area under the curve $y = x^2$ between $x = 1$, $x = 2$ and the $x…

Question

The area under the curve $y = x^2$ between $x = 1$, $x = 2$ and the $x$-axis is

Accepted Answer

D. $\frac{7}{3}$

1. Since $y = x^2 \geq 0$ on $[1, 2]$, area $= \int_1^2 x^2\,dx$.
2. $= \left[\frac{x^3}{3}\right]_1^2 = \frac{8}{3} - \frac{1}{3}$.
3. $= \frac{7}{3}$. (Using only the upper limit $\frac{8}{3}$ forgets to subtract the lower limit.)
_Source: NCERT Class 12 Mathematics Ch 8 "Application of Integrals", p.6_

Answer

$3$

Answer

$\frac{8}{3}$

Answer

$\frac{7}{2}$