8. Definite Integrals

Use five rectangles to estimate the area under the curve of $f\left(x\right)=x^2$ from $x=0$ to $x=5$ using left endpoints.

Use two rectangles to estimate the area under the curve of $f\left(x\right)=\frac{1}{2}{x}^2$ from $x=0$ to $x=3$ using left endpoints.

Use four rectangles to estimate the area under the curve of $f\left(x\right)=x^2+2$ from $x=0$ to $x=2$ using left endpoints.

Use three rectangles to estimate the area under the curve of $f\left(x\right)=\frac{1}{3}{x}^3$ from $x=0$ to $x=3$ using the right endpoints.