# How to find the integral of e^(sqrt(x)) as x goes from 0 to 1

1. Dec 20, 2007

### ricekrispie

1. The problem statement, all variables and given/known data

$$\int_0^1 e ^(sqrt. x) dx$$

2. Relevant equations

3. The attempt at a solution

i don´t know what to let u equal to... maybe sqrt.x? but what good would that do when u is differentiated?

2. Dec 20, 2007

### rocomath

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

yes?

3. Dec 20, 2007

### ricekrispie

yes, thanks... i´m still figuring out how to use it

4. Dec 20, 2007

### rocomath

Let u=$$\sqrt{x}$$

then, use another "simple" substitution so that you only have 1 variable.

then, you will need to use integration by parts.

5. Dec 20, 2007

### ricekrispie

i still haven´t figured the problem itself though...

6. Dec 20, 2007

### rocomath

shoot, at least you've already almost got it down. there are ppl with like 500+ posts and still don't use latek, hurts my eyes :p

7. Dec 20, 2007

### ricekrispie

that was before learning integration by parts so i guess i´m not supposed to use it

8. Dec 20, 2007

### rocomath

what technique are you not allowed to use?

9. Dec 20, 2007

### ricekrispie

integration by parts... thats why i´m stuck

10. Dec 20, 2007

### rocomath

there's no way around this problem without the use of integration by parts, want to work this problem together by use of parts?

11. Dec 20, 2007

### ricekrispie

do i let u = $$e^\sqrt{x}$$ ?

12. Dec 20, 2007

### rocomath

the derivative of your substitution would then become

$$u=e^{\sqrt{x}}$$

$$du=\frac{e^{\sqrt{x}}}{2\sqrt{x}}dx$$

messy. then you will need to take the ln of your u-substitution so you can get your problem in terms of 1 variable.

Last edited: Dec 20, 2007
13. Dec 20, 2007

### ricekrispie

so then u is just $$\sqrt{x}$$ ?

14. Dec 20, 2007

### rocomath

yes and i can help you through integration by parts, b/c we can't integrate this problem by simple substitutions.

15. Dec 20, 2007

### ricekrispie

ok... u = $$\sqrt{x}$$
and du = $$du=\frac{1}{2\sqrt{x}}dx$$

16. Dec 20, 2007

### ricekrispie

what would dv be?

17. Dec 20, 2007

### rocomath

well first, let's make it a "t-substitution" b/c we'll need to use U and V for parts.

so

$$dx=2\sqrt{x}dt$$

now we need our integration in terms of 1 variable, so

$$t=\sqrt{x}$$

thus

$$\int e^{\sqrt{x}}dx \rightarrow 2\int te^{t}dt$$

now we do integration by parts.

Last edited: Dec 20, 2007
18. Dec 20, 2007

### rocomath

no, the last step was a simple substitution ... this next step we will use parts.

19. Dec 20, 2007

### ricekrispie

wait.. i´m confused... now i have $$\sqrt{x}$$ as u
and then i have to square it?

Last edited: Dec 20, 2007
20. Dec 20, 2007

### rocomath

$$2\int te^{t}dt$$

$$\begin{array}{cc}u=t & dV=e^{t}dt \\ du=dt & V=e^{t}\end{array}$$

i'm sure you can take it from here! (judging from your other post)