Calc Integrals?

Question

Consider the given parabola. x=4y-y^2

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure) is given by the following integral. (Turn your head clockwise and think of the region as lying below the curve x = 4y - y2 from y = 0 to y = a = 4.)

4y-y^2 dy from 0 to 4

find the area

thanks

Answer 1

Well, they actually tell you what the integral is, so this is a trivial computation:

[0, 4]∫4y - y² dy
2y² - y³/3|[0, 4]
2(4²) - 4³/3
32 - 64/3
32/3