Application of Integrals

Find the area bounded by the curve y = x^2 and the line y = 4.

The area bounded by the curve y = sin x and the x-axis between x = 0 and x = \pi is:

Find the volume generated when the region bounded by y = x and y = x^2 is revolved about the x-axis between x=0 and x=1.

The area bounded by y = e^x, y = e^{-x}, and the y-axis is:

Find the volume of the solid generated when the region bounded by y = \sqrt{x}, y=0, and x=1 is revolved about the x-axis.

Find the area bounded by the curves y = x^3 and y = x.

The volume of the solid generated by rotating the region bounded by y = x^2 and y = 4 about the line y=4 is:

Find the area bounded by y = x and y = x^2 in the first quadrant.

The volume of the solid generated by revolving the region bounded by y = \sqrt{x}, x=4, and y=0 about the y-axis is:

Find the area bounded by the curves y = ln x, y=0, x=1 and x=e.