Area under a parabola

Text

Compute the area of the region bounded by the curve $y=x^{2}$, the $x$-axis and the lines $x=2$ and $x=4$.

Solution

$A=\displaystyle\int_2^4 x^{2}\,dx=\Big[\tfrac{x^{3}}{3}\Big]_2^4=\dfrac{56}{3}\approx18.667$. $\boxed{A=\tfrac{56}{3}\approx18.667}$