Find the area under the curve in the function below from $x=-4$to $x=8$.

Use 3 rectangles to approximate the area under $f\left(x\right)=x^2$ from $x=2$to $x=5$ with right endpoints.

Use 6 rectangles to approximate the area under $f\(\left\)(x\(\right\))=x^3$ from $x=0$ to $x=3$ with left endpoints.

Find the area under the curve, of the function $f\left(x\right)=3x+2$ from $x=0$ to $x=4$ using limits.

Find the area under the curve, of the function $f\left(x\right)=x^2$ from $x=0$ to $x=8$ using limits.