# solids of revolution/integration question

• January 3rd 2010, 06:01 PM
shawli
solids of revolution/integration question
The volume of the solid formed when the region bounded by the curve $y = e^x - k$ , the x-axis and the line $x=ln3$ is rotated about the x-axis is $pi*ln3$ units cubed. Find k.
• January 3rd 2010, 06:14 PM
skeeter
Quote:

Originally Posted by shawli
The volume of the solid formed when the region bounded by the curve http://www4c.wolframalpha.com/Calcul...image/gif&s=48, the x-axis and the line x=ln3 is rotated about the x-axis is pi*ln3 units cubed. Find k.

is the function $y = e^{x-k}$ or $y = e^x - k$ ?
• January 4th 2010, 03:32 PM
shawli
Quote:

Originally Posted by skeeter

is the function $y = e^{x-k}$ or $y = e^x - k$ ?

The second one, $y = e^x - k$.
• January 4th 2010, 03:55 PM
skeeter
Quote:

Originally Posted by shawli
The second one, $y = e^x - k$.

any other information about the constant k ?
• January 4th 2010, 06:54 PM
shawli
Nope, that is the question exactly as it is given. I could post the answer at the back of the text book if you'd like to verify your solution though?
• January 4th 2010, 07:15 PM
mr fantastic
Quote:

Originally Posted by shawli
The volume of the solid formed when the region bounded by the curve $y = e^x - k$ , the x-axis and the line $x=ln3$ is rotated about the x-axis is $pi*ln3$ units cubed. Find k.

Solve $\int_{\ln k}^{\ln 3} (e^x - k)^2 \, dx = \ln 3$ for $k$. I get k = 1.