AP Calculus BC / Unit 8: Applications of Integration
8.12 Volume with Washer Method: Revolving Around Other Axes
Notes
Measure both radii from the axis line:
- Around $y=k$ below the region: $R=\text{top}-k$, $r=\text{bottom}-k$.
- Around $y=k$ above the region: $R=k-\text{bottom}$, $r=k-\text{top}$.
Practice
Region between $y=x$ and $y=x^2$ on $[0,1]$, revolved around $y=-1$. Outer radius:
The far curve from $y=-1$ is $y=x$.
Same region, around $y=2$. Outer radius:
The far curve from $y=2$ is the lower curve, $y=x^2$.
Same region, around $y=2$. Inner radius:
The near curve is $y=x$.
Ready for more? Take the Unit 8 test.