Definite integration by U subsitution

1. Nov 30, 2012

steel1

1. The problem statement, all variables and given/known data
4
∫√(t)(10+t)(dt)
1

note, only the t is under the square root.
2. Relevant equations

3. The attempt at a solution
Ok. I have to solve this integration problem by U substitution.
To start, I am not entirely sure what to even set U equal to. I let it equal the number under the square root.

So,

U=t
Du=dx

But where do i go after this?

2. Nov 30, 2012

Zondrina

Hey there, welcome to PF.

Your substitution is wrong, and your derivative as well. You should've gotten u = t so du = dt.

That will still be wrong though.

Try the substitution u = $\sqrt{t}$.

3. Nov 30, 2012

steel1

ok. If i set U=√t and Du=dt, where do i go from there? the du=dx was a typo.

4. Nov 30, 2012

haruspex

No, if u=√t du will not equal dt. For the purposes of figuring out the substitution for dt it will be more helpful to write the substitution as u2=t. What does that give when you differentiate?

5. Nov 30, 2012

steel1

derivative of u^2=t is 2u=1?

6. Nov 30, 2012

steel1

If somebody could just do the entire thing via U substitution, that would be great. Then I can see how you did it. I'll be refreshing this page every few minutes.

7. Nov 30, 2012

Staff: Mentor

That's clear from the parentheses you have.
This is NEVER a good substitution, since all you're doing is changing to a different letter. Also, the second line should be du = dt, not du = dx.

8. Nov 30, 2012

Staff: Mentor

Do you have to use a substitution?

If not, rewrite the integrand this way:
√(t) (10 + t) = 10√(t) + t√(t) = 10t1/2 + t3/2

9. Nov 30, 2012

steel1

Yeah, this is what i have so far

U^2=t

2du=dt

10. Nov 30, 2012

steel1

yes, i would prefer to solve this by u substitution, so i can see how its done.

11. Nov 30, 2012

Staff: Mentor

No on two counts. First, you're not taking derivatives - you're getting the differentials of u2 and t.

Second, the differential of t is dt, not 1.

Here's how it works for both sides:

d(u2) = d(u2)/dt * dt = 2u * du
d(t) = d(t)/dt * dt = 1 * dt

You're new here, so there's a good chance you haven't looked at the forum rules, even though you said you did when you signed on. Take a look at the rules by following the link, especially the Homework Help section.

You'll see that we won't do the work for you, but we'll help you do the work by guiding you in the right direction.

12. Nov 30, 2012

Staff: Mentor

OK, that's a reasonable reason. Follow the suggestions made by Zondrina and haruspex.