AP Calculus BC 8.11 Washer Method Overview

Set up washer-method volume integrals by expressing outer and inner radii relative to the chosen axis of rotation, with correct bounds and subtraction order.

Exam points

identify the governing calculus relationship in the problem
justify the result with symbolic, graphical or contextual evidence

Covered syllabus points

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

[Maximum number: 1]

Let R be the region in the first quadrant bounded by the graph of $y=\sqrt{x-1}$ , 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?

$\pi \int_{1}^{10}(x-1) d x$

$\pi \int_{1}^{10}(100-(x-1)) d x$

$\pi \int_{0}^{3}\left(10-\left(y^{2}+1\right)\right)^{2} d y$

$\pi \int_{0}^{3}\left(100-\left(y^{2}+1\right)^{2}\right) d y$

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Covered syllabus points

8.11 Volume with Washer Method: Revolving Around the x- or y-Axis question 1