I try to solve it, but I don\'t know why the question b is wrong. o AT&T; LTE 13

Question

I try to solve it, but I don't know why the question b is wrong. o AT&T; LTE 13:14 gauchospace.ucsb.edu (1 pt) Consider the solid under the graph of z = e above the disk x2 + y2 0 (a) Set up the integral to find the volume of the solid. Instructions: Please enter the integrand in the first answer box, typing theta for . Depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. Then, enter the limits of integration. dr dtheta B= 2pi (b) Evaluate the integral and find the volume. Your answer will be in terms of a Volume V= (c) what does the volume approach as a oo? lim V- pi

Explanation / Answer

in poalr coordinates

x=rcos y=rsin

x2+y2=r2

x2+y2<=a2

0<=<=2,0<=r<=a

dv =r dr d

z=e-x^2-y^2=e-r^2

volume v= [0 to 2][0 to a]e-r^2r dr d

v= [0 to 2][0 to a](-1/2)e-r^2 d

v= [0 to 2](-1/2)e-a^2 -(-1/2)e-0^2 d

v= [0 to 2](-1/2)e-a^2 +(1/2) d

v= [0 to 2](1/2)(1-e-a^2) d

v= [0 to 2](1/2)(1-e-a^2)

v=(1/2)(1-e-a^2)(2-0)

v=(1-e-a^2)

c)lima->V

=lima->(1-e-a^2)

=(1-0)

=

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