Area of region example
Find area of region bounded by parabola x = y2 and the line y = x.
Graph:

We’ll let y go from 0 to 1. Then x goes from y2 to y.
Area is
| ∫ 01 ∫ y2ydxdy | = ∫
01 dy | ||
| = ∫ 01(y - y2)dy | |||
= ![]() -![]() 01 | |||
= - = ![]() |
Note: if asked to integrate a function f(x,y) over that region, you’d need to compute
| ∫ 01 ∫ y2yf(x,y)dxdy. |



![]](doubleintareaex5x.png)
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