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 $f\left(x\right)=\frac12x^2$ 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 $f\left(x\right)=\frac13x^3$ from $x=0$ to $x=3$ using the right endpoints.

Use three rectangles to approximate the area under the curve of $f\left(x\right)=3\left(x-2\right)^2$ from $x=0$ to $x=3$ using the midpoint rule.