AP Calculus BC 8.12 Volume with Washer Method Revolving Around Other Axes Questions

Review washer-method questions by finding outer and inner radii relative to a shifted axis before integrating and checking which radius is larger.

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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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