Find the volume of the solid formed by rotating the region enclosed by

Question

y=e^4x+3 y=0 x=0 x=0.7

this is my work

V = ∫ e^4x dx {between x=0 and x=0.7}
= 1/4 e^4x {between x=0 and x=0.7}
= 1/4 (e^2.8 - e^0)
= 1/4 (e^2.8 - 1)

however i am etting the wrong answer pls help!!!

Answer 1

What you have found is the area of the region.
But you wanted the volume.
We also have to assume you are rotating about the x-axis.

in general V = pi∫ y^2 dx

so you want
V = pi∫e^8x dx from 0 to .7
= (1/8)pi[e^8x] from 0 to .7
= (1.8)(pi(e^5.6 - e^0)
= 105.8

You better check my arithmetic.

Answer 2

Hi i checked the arithmitic and got 154.3699603 but this does not seem to be the right answer either what should I do??

Answer 3

Arggghhh!! I forgot the + 3 in the equation

try this
V = pi∫(e4x+x3)^2 dx from 0 to .7
= pi∫(e^8x + 6e^4x + 9)dx
= pi[(e^8x)/8 + (3/2)e^4x + 9x) from 0 to .7

= .... I will leave the arithmetic up to you, let me if it worked out this time.