Science:Math Exam Resources/Courses/MATH101/April 2017/Question 02 (a)/Solution 1

From UBC Wiki

We consider the region between two curves and .

First, we find the intersection points. Since two curves can be written as and , plugging the first one into the second one, we get

Therefore, the intersection points are and .

On the other hand, according to the question, the curve lies on the right side of , so that when .

To summarize, the area between the two curves has to be an integral of the form

The last equality follows from the fact that is even. Therefore, the answer is .

Answer: .