## Dido525 2 years ago Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the specified axis. y = 7e^x, y = 7e−x, x = 1; about the y-axis

1. Dido525

I don't get what I did wrong in my work. Let me post it.

2. Dido525

|dw:1358999196019:dw|

3. Dido525

Did I set up the integral properly?

4. Dido525

@Mimi_x3 @satellite73

5. tkhunny

What did you get for your points of intersection? y = 7e^x vs x = 1 is obviously (1,7e) y = 7e−x vs x = 1 is obviously (1,7e-1) But what about y = 7e^x vs y = 7e−x ? Since this cannot be solved by direct methods, we get (0.9488478,18.0791250) Maybe the problem statement is not written correctly?

6. Dido525

Let me send a pic.

7. Dido525

8. Dido525

I used the e points of intersection so I used 0 to 1.

9. Dido525

x not e.

10. tkhunny

$$y = 7e^{x}$$ -- You wrote this one okay. $$y = 7e^{-x}$$ -- This is quite a different story. Please learn to code LaTeX or to use the Equation Editor. It will be a great benefit to you now and in the future. You're f(x) is not correct. You just picked one of the curves. You need the distance between them.

11. Dido525

Ohh I can write in latex. It just takes too long lol.

12. tkhunny

It would have avoided much time and error. 7e-x is VERY different from 7e^(-x) or $$7e^{-x}$$

13. Dido525

So I wrote my integral as: $14\pi \int\limits_{}^{}xe^x dx$

14. Dido525

How do I incorporate the e^-x then?

15. tkhunny

$$e^{x}$$ is no good. You need $$e^{x} - e^{-x}$$.

16. Dido525

Huh? Why?

17. Dido525

Nevermind. I see why.

18. Dido525

The limits of intergation should still be the same right?

19. tkhunny

Did you draw a picture? The height of your cyllinders is the difference of the two curves.

20. Dido525

Yeah I did, One moment.

21. Dido525

|dw:1359002030111:dw|

22. Dido525

Something like that.

23. tkhunny

That's it. And the final answer is?

24. Dido525

I see why it's the difference though.

25. Dido525

Sec.

26. Dido525

$\frac{ 28\pi }{ e}$ is what I got.

27. tkhunny

I like it. Now, your punishment for writing one of the equations incorrectly in the beginning is to find the point of intersection for what you wrote. Find the value of x such that $$7e^{x} = 7e - x$$. It's a wonderful exploration.

28. Dido525

Eww... Natural logs...

29. tkhunny

No, no. It's far worse than that. :-) When you are ready...

30. Dido525

Ahh I see... Hehe...

31. Dido525

Yeah... I have to use a calculator lol.