## bettyboop8904 2 years ago Can someone give me a quick recap of integrals? I have an example and there are 5 problems that are done similarly. Example is in the post with equation converter helper.

1. bettyboop8904

$\int\limits_{0}^{1} (9x ^{e}+e ^{x})dx$ Do I use u substitution?

I can't tell what the power of x is but it looks like an e? Either way, you can break this integral into two parts. $\int\limits_{0}^{1}9x^e + \int\limits_{0}^{1}e^x$ Then just take integrate the individual integrals.

The rule of integration for X^n where n is a constant is $x^{n+1}/(n+1)$ And the integral of e^x is just e^x

4. bettyboop8904

Wait I'm confused on the last post. $\frac{ x ^{n+1} }{ n+1 }$ Isn't that the anti-derivative?

5. bettyboop8904

is that what an integral is?

Exactly! An integral is the anti-derivative.

7. hartnn

recap of integrals ? try this.... http://openstudy.com/users/hartnn#/updates/50960518e4b0d0275a3ccfba

Well not exactly, but a key component of taking the integral of something is finding the anti-derivative. If there are no bounds, then an integral is essentially the anti-derivative.

9. bettyboop8904

Oh ok = ) So that's how you solve an integral. you use the rule that you can split the integrals up and then solve each one by finding the anti-derivative. Oh yeah bc you have to incorporate the integral 0 to 1 right?

10. bettyboop8904

so does that mean you would have: $\frac{ 9x ^{e+1} }{ e+1 }$ and $\frac{ e ^{x+1} }{ x+1 }$ is that right?

11. hartnn

the first part is correct, for e^x $$\int e^xdx=e^x+c$$

But since this is a definite integral (it has bounds) you can ignore the c, which will cancel out anyway.

13. bettyboop8904

oh yeah that's right because the integral of e^x is itself right?

Yup

15. bettyboop8904

Ok so what's next? or is that all I have to do with it?

16. bettyboop8904

It just says evaluate the integral

Once you've taken the anti-derivative of it you plug in your bounds for x So for the integral of e^x for example: you'd get $e^1 - e^0$ Which simplifies into e-1 But you have to remember that you're adding this to the integral of the first half.

18. bettyboop8904

Oh wait I just realized I typed the problem out. There is no 9 in front of the x^e

19. bettyboop8904

*typed it out wrong lol

The answer you posted above was correct for the anti-derivative of x^e, just take out the 9 then.

21. bettyboop8904

stupid question how do you get e^-1 from e^1-e^0?

so e^1 = e e^0 = 1 So e^1 - e^0 = e - 1

23. bettyboop8904

oh ok I thought the -1 was the exponent of e from the rule of two bases being the same the exponents divide you know what I'm trying to say? lol