# I don't understand this integral

1. Mar 11, 2007

### jkh4

I don't understand for integral ysin(xy)dx = -cos(xy) for a=1 b=2. I know sin's integral is cos, but I don't understand how to eliminated the y in the left equation so it become the right equation. Please help!

2. Mar 11, 2007

### JasonRox

What is the derivative to -cos(xy)?

That should help to where the y is going.

3. Mar 11, 2007

### nrqed

I am assuming that the a and b are the limits of integration.
And I am assuming that y is a constant here (it's independent of x). Then this is the simplest type of substitution: just define a new variable z=xy. What is dx then? You should then integrate easily (watch out about changing the limits of integration though if you leave your answer in terms of z).

4. Mar 11, 2007

### jkh4

how do you integrate x(y^2 - x^2)^(1/2)? my TA says the answer is (-1/3)((y^2 - x^2)^(3/2)) but i don't get where is the (-1/3) comes from....

5. Mar 11, 2007

### JasonRox

Did you not do any substitution rules or anything?

Where is the work for this? Follow the work and it should be clear where it came from.

6. Mar 11, 2007

### jkh4

this is the process i got so far

(x^2/2)((y^2-x^2)^(3/2))/(3/2)(-1/x^2)

but one thing i don't understand, for the (-1/X^2), is this a proper intergral step?

7. Mar 11, 2007

### JasonRox

What?

Where does all this come from?

8. Mar 11, 2007

### jkh4

nevermind , i got it

Last edited: Mar 11, 2007
9. Mar 12, 2007

### HallsofIvy

Staff Emeritus
One thing that was causing confusion throughout this thread- it was never stated that the integration was to be done with respect to x!