AP Calculus AB / Unit 8: Applications of Integration
8.5 Finding the Area Between Curves Expressed as Functions of y
Notes
$$A=\int_c^d [\text{right}(y)-\text{left}(y)]\,dy$$
- Useful when curves are given as $x=g(y)$ or when slicing horizontally avoids splitting the region.
Practice
Area between $x=y^2$ and $x=4$:
$\displaystyle \int_{-2}^2(4-y^2)dy$.
When integrating with respect to $y$, you subtract:
Horizontal slices run left to right.
Area between $x=y$ and $x=y^2$ for $0\le y\le1$:
$\displaystyle \int_0^1(y-y^2)dy$.
Ready for more? Take the Unit 8 test.