# I don't understand this integral

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!

## Answers and Replies

JasonRox
Homework Helper
Gold Member
What is the derivative to -cos(xy)?

That should help to where the y is going.

nrqed
Science Advisor
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Gold Member
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!

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).

what about this one?

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....

JasonRox
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what about this one?

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....

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.

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?

JasonRox
Homework Helper
Gold Member
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?

What?

Where does all this come from?

nevermind , i got it

Last edited:
HallsofIvy
Science Advisor
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One thing that was causing confusion throughout this thread- it was never stated that the integration was to be done with respect to x!