You don’t have the endpoints this time, so you need to find where the two curves intersect. If you set them
equal to each other, they intersect at y = 0 and at y = 5. The curve x = y^2 − 4y is always to the left of x = y
over the interval we just found, so we can evaluate the following integral:
[y − (y^2 − 4y)] dy = (5y − y^2 ) dyThe result of the integration should be
PROBLEM 4. Find the area between the curve x = y^3 − y and the line x = 0 (the y-axis).
Answer: First, sketch the graph over the interval.