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 = ex - (-1) = ex +1
distance from the bottom curve to the axis of rotation = 1 - (-1) = 2
The left bound is the x-value where y = ex crosses y = 1, which is at x = 0. The right bound is the x-value where y = ex and y = 1 cross x = 2, which is at x = 2. The integral will be taken from x = 0 to x = 2.
V = π ∫ [(ex +1)2 - (2)2] dx
You answer is D