AP Calculus BC 8.12: Washer Method

Practice AP Calculus BC questions on writing a washer-method volume integral when a region rotates around a horizontal or vertical line.

[Maximum number: 3]

Let R be the shaded region bounded by the graph of $y=x e^{x^{2}}$ , the line y=-2 x, and the vertical line x=1, as shown in the figure above.

Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y=-2.

Volume $=\pi \int_{0}^{1}\left[\left(x e^{x^{2}}+2\right)^{2}-(-2 x+2)^{2}\right] d x$

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CHA-5.C—Calculate volumes of solids of revolution using definite integrals—Topic 8.12 question 1