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AP Calculus BC 8.11: Washer Method

Practise AP Calculus BC 8.11 by choosing inner and outer radii, setting bounds in the correct variable, and evaluating washer-method volume integrals.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Exam points

  • Set up π∫(R²−r²) using the correct inner and outer radii for rotation about an axis.
  • Choose x- or y-integration bounds so the washer slices stay perpendicular to the rotation axis.

CHA-5.C—Calculate volumes of solids of revolution using definite integrals—Topic 8.11 question 1

[Maximum number: 1]

Let R be the region in the first quadrant bounded by the graph of y=x−1y=\sqrt{x-1}, the x-axis, and the vertical line x=10. Which of the following integrals gives the volume of the solid generated by revolving R about the y-axis?

A

π∫110(x−1)dx\pi \int_{1}^{10}(x-1) d x

B

π∫110(100−(x−1))dx\pi \int_{1}^{10}(100-(x-1)) d x

C

π∫03(10−(y2+1))2dy\pi \int_{0}^{3}\left(10-\left(y^{2}+1\right)\right)^{2} d y

D

π∫03(100−(y2+1)2)dy\pi \int_{0}^{3}\left(100-\left(y^{2}+1\right)^{2}\right) d y

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