14. 15. Find the area bounded by y=-x² and y=2x. Find the average value of y=4x³ + 2x over [-2,5].

A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.

The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?

A curve is such that the area bounded between the curve, the y-axis, the x-axis and the line parallel to the x-axis passing through P(x, y) is equal to x + y. Find the equation of the curve.