hw 10 question 9

Question

Find the volume generated by revolving about the x-axis the regions bounded by the following graphs.

y = e^x

x = -2

x = 3

Answer 1

V = π ∫³ _-2 [e^x]² d x = (π/2) [e^2x] |³_-2 = (π/2)[ e⁶-e^-4] ≈ 633.676 cubic units

Answer 2

integrate pi(r^2) = integral of pi(e^x)^2 = integral of pie^2x = pie^2x/2

(integral of e^x is itself, e^x.

derivative of e^x = e^x)

then evaluate between -2 and 3

= about 633.7

(pi/2)[e^6-e^-4) = 1.571(403.43 - .02) = 1.57(403.41) = about 633.7