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(5 points) Consider the (unbounded) region R in the first quadrant consisting of the area under the curve y = 1 and to the left of the curve x = ln(e/y) (see diagram below). Let V be the volume of the solid generated by revolving R about the y-axis. Set up two expressions for V , one that uses the slicing/washer method and one that uses the cylindrical shells method. Choose one of these methods to determine the exact value of V . Show all your work (note that you need to compute an improper integral).

(5 points) Consider the (unbounded) region R in the first quadrant consisting of the area under the curve y = 1 and to the left of the curve x = ln(e/y) (see diagram below). Let V be the volume of the solid generated by revolving R about the y-axis. Set up two expressions for V , one that uses the slicing/washer method and one that uses the cylindrical shells method. Choose one of these methods to determine the exact value of V . Show all your work (note that you need to compute an improper integral).

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  1. (5 points) Consider the (unbounded) region R in the first quadrant consisting of the area under the curve y = 1 and to the left of the curve x = ln ⁡ ( e / y ) (see diagram below).
    Let V be the volume of the solid generated by revolving R about the y -axis. Set up two expressions for V , one that uses the slicing/washer method and one that uses the cylindrical shells method. Choose one of these methods to determine the exact value of V .
    Show all your work (note that you need to compute an improper integral).

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