1. Need to find the area between the graph and the x-axis on the interval y=X^3-3x^2-10x [-2,5]
2. Find the average value of y=X^3+4/ x^2 over [2,4]
3. Find the area of the region bounded by y=2x^2-4x-4 and y=-2x+8

For #1, just integrate y with respect to x with the limits of integration being the interval shown.

For #2, just find the integral of the function with respect to x, over the interval shown. Then divide by the width of the interval (4-2=2).

For #3, find the two intersecting points of the two functions, and then integrate both functions with respect to x over the interval that corresponds to the intersecting points. Then take the resulting value from the integral for the function that is graphically on top, and subtract the value from the integral for the function that is graphically on the bottom.

I used to tutor all the time, so I don't like to do the work explicitly, but I can help if need be.

This post was edited by xRiemensverax on Jul 7 2015 10:10pm