Janelle S. answered • 09/23/20

Penn State Grad for ME, Math & Test Prep Tutoring (10+ yrs experience)

V = π ∫ [f(x)^{2} - g(x)^{2}] dx

where f(x) is the top curve, g(x) is the bottom curve, and dx is the width

distance from the top curve to the axis of rotation = e^{x} - (-1) = e^{x} +1

distance from the bottom curve to the axis of rotation = 1 - (-1) = 2

The left bound is the x-value where y = e^{x} crosses y = 1, which is at x = 0. The right bound is the x-value where y = e^{x} and y = 1 cross x = 2, which is at x = 2. The integral will be taken from x = 0 to x = 2.

V = π ∫ [(e^{x} +1)^{2} - (2)^{2}] dx

You answer is D