# Double integral

1. Mar 15, 2006

### thenewbosco

Perhaps someone can explain how to do, or a trick to solve this integral:

$$\int_{0}^{3}\int_{\sqrt{y+1}}^{2} \frac{e^x}{x+1}$$ dx dy

i dont know if $$\frac{e^x}{x+1}$$ has an elementary antideriv. so there should be some trick to solving this i guess....

Last edited: Mar 15, 2006
2. Mar 15, 2006

### Hurkyl

Staff Emeritus
You have to use '_' and '^' to set the limits on an integral. e.g.

\int_{lower}^{upper}

And you forgot to put your dx's and dy's in the problem.

The first thing I think of when I'm stumped on a double integral is to reverse the order of integration to see if that helps. Have you tried that?

Last edited: Mar 15, 2006
3. Mar 15, 2006

### thenewbosco

right there it is correctly formatted. but by reversing the order, you will have a y in the final answer, not like it helps to reverse in this case anyways

4. Mar 15, 2006

### Hurkyl

Staff Emeritus
Well, when you reverse the order, the limits change, right? You won't know if it helps until you try it!

5. Mar 15, 2006

### buzzmath

use integration by parts.

Last edited: Mar 15, 2006
6. Mar 15, 2006

### thenewbosco

what do you choose for u and dv? i cannot simplify it?

7. Mar 15, 2006

### buzzmath

try using u = x+l and dv=e^xdx then du=dx and v=e^x
do you know the formula for integration by parts?

8. Mar 15, 2006

### shmoe

Have you, thenewbosco, followed this advice yet?

9. Mar 15, 2006

### thenewbosco

if you try this you get 3*e^x/(x+1) which doesnt really help any?

10. Mar 15, 2006

### shmoe

When you change the order of integration, you have to be careful with the limits. It might help if you sketch the region you are integrating over. What is the integral after you change the order?

11. Mar 16, 2006

### HallsofIvy

Staff Emeritus
Since the problem is
$$\int \frac{e^x dx}{x+1}$$
rather than
$$\int (x+1)e^x dx$$
that doesn't help at all.

Changing the order of integration is the way to go.

Thenewbosco, have you sketched the area over which you are integrating? That's the best way to find the new limits of integration. Once you've done that you can use buzzmath's suggestion of integration by parts but with u= x-1, not x+1!