# Thread: Perimeter of a Region

1. ## Perimeter of a Region

How do I find the perimeter of the region bounded by $\displaystyle y=e^x, y=0, x=0,$and $\displaystyle x=1$?

Mainly I need to know how to find the length of $\displaystyle e^x$ from 0 to 1. I know that once I get this number I can just add the other sides (1, 1, and e^1).

2. Originally Posted by ZosoPage
How do I find the perimeter of the region bounded by $\displaystyle y=e^x, y=0, x=0,$and $\displaystyle x=1$?

Mainly I need to know how to find the length of $\displaystyle e^x$ from 0 to 1. I know that once I get this number I can just add the other sides (1, 1, and e^1).
arc length of a function f(x) ...

$\displaystyle S = \int_a^b \sqrt{1 + \left[f'(x)\right]^2} \, dx$

3. so

$\displaystyle \int_{0}^{1}\sqrt{1+e^{2x}}dx$

where do I go from here?

4. Originally Posted by ZosoPage
so

$\displaystyle \int_{0}^{1}\sqrt{1+e^{2x}}dx$

where do I go from here?
your lack of knowledge in solving this and other basic calculus problems at this level is fairly evident.

are you presently enrolled in a calculus class?

5. Yes I am, but I'm having a lot of trouble recently. I understood it all first semester but now the teacher does not explain things to us and she will not respond to e-mails when I ask her questions. Whenever I ask her things in class, she always has "somewhere she has to be" and says to email her my questions. That is why I came here to get help.

6. Originally Posted by ZosoPage
so

$\displaystyle \int_{0}^{1}\sqrt{1+e^{2x}}dx$

where do I go from here?
option 1 ... use technology to evaluate the integral.

option 2 ... substitution, $\displaystyle u^2 = 1 + e^{2x}$ . the process will involve partial fractions and the exact solution is rather ugly.

option 3 ... trig substitution, $\displaystyle e^x = \tan{\theta}$ . process will involve integration by parts.

there may be other methods.