Question

HELP: INTEGRATION!!!
Best answer gets MEDAL + FAN + TESTIMONIAL.

Answer 1

Question?

Answer 2

Wait a second I have to type it up.

Answer 3

\(\int_ x ^(x+ 5) \sqrt{ 1 + e^u} dx\)

Answer 4

@iambatman

Answer 5

The x + 5 is the upper limit of the integral.

Answer 6

?

Answer 7

Have you tried anything?

Answer 8

Yes i used the 2nd part of the theorem of calculus but it wasn't right.

Answer 9

I think its because there are functions in both boundaries. I don't know how to attempt this.

Answer 10

I'll be honest, I've never done an integral like the one you represent.

Answer 11

Oh, alright. Do you know anyone else who can here?

Answer 12

Oh yay, mathmale is here :)!

Answer 13

\[\int\limits_ x ^(x+ 5) \sqrt{ 1 + e^u} dx \rightarrow \int\limits_{x}^{x+5}\sqrt{1+e^u}dx\]frankly looks very odd in that you have two different variables in the integrand (x and u), and your limits of integration are functions of x.

This would make more sense to me were you integrating with respect to u, not with respect to x. Are you positive that you've copied this problem down correctlly?

Also, are you positive that the end goal is to INTEGRATE? I'd be willing to bet that the goal of this problem is to find the DERIVATIVE of this function defined as an integral.

Answer 14

It's with respect to u.

Answer 15

Sorry for the error.

Answer 16

It's the derivative of the integral as well.

Answer 17

If (and only if) my hunch is correct, and you're supposed to differentiate a function defined as a definite integral, then you'll need to break this integral into two parts:
First: the integral from x to 0. Second: the integral frmo 0 to x+5.

You'll need to differentiate each of these two integrals separately, and then combine the results of that differentiation. Care to give these steps a try?

Answer 18

I don't know how to find an integral from x to 0.

Answer 19

Note that the Fundamental Theorem section that applies to this type of problem (derivative of a function defined as a definite integral) assumes that we integrate from a constant to either x or some function of x.

In YOUR math problem, both limits of integration are functions (one is x, the other is x+5).

Answer 20

So: we have to break up this integral as previously mentioned, obtaining\[\int\limits_{x}^{0}\sqrt{1+e^u}du+\int\limits_{0}^{x+5}\sqrt{1+e^u}du\]

Answer 21

Yes but does \(\int _ x ^ 0 \sqrt{1 + e^2}du = -\int _ 0 ^ x \sqrt{1 + e^2} \) ?

Answer 22

...and there is another property that says we can re-write the first term (above) as\[-\int\limits_{0}^{x}\sqrt{1+e^u}du\]

Answer 23

\(e^u\)**

Answer 24

Oh so I'm right?

Answer 25

You're on the right track; that's for sure!

Answer 26

Now, would you attempt to evaluate the first of these two terms? In other words, evaluate \[-\int\limits\limits_{0}^{x}\sqrt{1+e^u}du\]

Answer 27

f(g(x)) * g'(x)?
Where g(x) is x and f(x) is \(\sqrt {1+e^u}\)

Answer 28

I agree with that. Good. Focus on the square root expression. Replace u with x. Don't forget to keep that negative sign. What do you get? (Note: the derivative g'(x)=1 here.)

Answer 29

And I would get \(\sqrt{1 + e^(x+5)}\)?

Answer 30

Yes. That would be the result of evaluating the 2nd term from above.

So, why not write your most recent term first and then subtract from it your previous term: Please write this out here for verification. Note: You're doing very well!

Answer 31

Can I write full answer because i know how to deal with the second term?

Answer 32

Of course, by all means proceed!

Answer 33

So its \(\sqrt{ 1+ e^(x+5)} - \sqrt{1 + e^x}\)?

Answer 34

Except for the formatting, that's exactly how I would write my answer to this problem. Nice work!

Answer 35

It never works when i put a power with two terms over a pronumeral -.-

Answer 36

It is ok if you help me with another?

Answer 37

Please, would you post your next question as a separate question? Thanks.