Application of Integral

What is the area under the curve y=x² from x=0 to x=2?

What is the volume of the solid obtained by rotating the region bounded by y=x and y = 0 from x=0 to x=1 around the x-axis?

What is the average value of the function f(x)=x+1 over the interval from x=1 to x=3?

If the velocity of an object is given by v(t)=3t² , what is the displacement of the object from t=0 to t=2?

What is the work done by a variable force F(x)=2x over the interval from x=1 to x=3?

The area under the curve y = \sqrt {x} from x = 0 to x = 4 is:

The centroid of the semicircle [Tex]y = \sqrt{r^2 - x^2}[/Tex] lies on: