Question

The area bounded by the curve $y=x^2+4$, the x-axis and the ordinates $x=1$ and $x=4$ is units.

Answer 1

The required area A is entirely above the x-axis, so we can simply evaluate the integral between the required limits.

$A={\int }_1^{4}ydx$
$A={\int }_1^4(x^2+4)dx$
$A={[\frac{x^3}{3}+4x]}_1^4$
$A=[\frac{64}{3}+16]-[\frac{1}{3}+4]$
$A=33$ units