Definite integration by U subsitution

[steel1]

Homework Statement

4
∫√(t)(10+t)(dt)
1

note, only the t is under the square root.

Homework Equations

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?

 

[STEMucator]

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}.

 

[steel1]

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

 

[haruspex]

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

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?

 

[steel1]

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

 

[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.

 

[Mark44]

Homework Statement

4
∫√(t)(10+t)(dt)
1

note, only the t is under the square root.

That's clear from the parentheses you have.

Homework Equations

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

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.

But where do i go after this?

 

[Mark44]

Do you have to use a substitution?

If not, rewrite the integrand this way:
√(t) (10 + t) = 10√(t) + t√(t) = 10t^1/2 + t^3/2

 

[steel1]

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.

Yeah, this is what i have so far

U^2=t

2du=dt

 

[steel1]

Do you have to use a substitution?

If not, rewrite the integrand this way:
√(t) (10 + t) = 10√(t) + t√(t) = 10t^1/2 + t^3/2

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

 

[Mark44]

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

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

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.

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.

 

[Mark44]

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

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