Find the area between
y = 5x^3 and the line y = 45x, for x 0
Can anybody show me how to go about doing this?
First you need to figure out where the curves intersect. So you have the equation or . Simplifying, expanding and solving for x:
So the curve has three roots. But the problem asks us only to consider values of x greater than or equal to 0, so we have the points of intersection at x = 0 and x = 3.
The next question is, which of the two curves is above the other? A quick test reveals where so it must be that is above . Hence, you want to use .
So to compute the area between the curves we integrate
.