Homework Help: Question about and request for a certain type of integration problem

1. Jun 5, 2012

NewtonianAlch

1. The problem statement, all variables and given/known data
http://img806.imageshack.us/img806/9455/67043570.jpg [Broken]

3. The attempt at a solution

http://img443.imageshack.us/img443/2449/50431877.jpg [Broken]

The part I got confused at was during the substitution.

I understand that there is a bound change (1,9) because we just sub in the values of y (0, 4) into t. What I got confused about was what happened to the y^(1/2) in dt. To be honest, I've not encountered a problem like this before, usually when making the substitution I've only ever had to get rid of constants hanging around.

Also, pointers to any other problems like this would be very helpful!

Last edited by a moderator: May 6, 2017
2. Jun 5, 2012

clamtrox

Maybe the square root of y is missing from the expression. Can you show the steps you take to get from two integrals to one?

3. Jun 5, 2012

clamtrox

There is a typo in the problem: the integration limit $\sqrt{4}$ should be $\sqrt{y}$

4. Jun 5, 2012

NewtonianAlch

No, it's not missing, those are the steps given in the solutions.

To reduce it to one integral you basically just integrate the first inner integrand, since the order is reversed, that means it becomes x ln ( 1 + y^(3/2)), and substituting the new bounds you will get that remaining integral.

I think to get 2/3 du, they just solve for y^(1/2)dy = 2/3du in the du equation, but that doesn't explain what happens to the constant 2 in the expression.

5. Jun 5, 2012

NewtonianAlch

Yes, it is sqrt(y), I just eliminated the initial stuff from the copy because I felt that people would realise that along the way, sorry for any confusion.

6. Jun 5, 2012

clamtrox

So when you take this typo into account, it all works out perfectly.

7. Jun 5, 2012

NewtonianAlch

I'm not sure I quite follow how it's a typo though?

8. Jun 5, 2012

NewtonianAlch

Oh...I see now! Gee, that really had me going. Thanks a lot!