Question

Use a definite integral to find the area of the region between the curves $y=x^2+x$ and the $x-$axis on the interval $[1,4]$

Answer 1

$A={\int }_1^4{x}^2+xdxA={[\frac{x^3}{3}+\frac{x^2}{2}]}_1^{4}A=\frac{4^3}{3}+\frac{4^2}{2}-[\frac{1^3}{3}+\frac{1^2}{2}]A=\frac{63}{3}+\frac{15}{2}A=\frac{157}{2}squnits$