I don't understand this integral

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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!
 

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  • #2
JasonRox
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What is the derivative to -cos(xy)?

That should help to where the y is going.
 
  • #3
nrqed
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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).
 
  • #4
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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....
 
  • #5
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.
 
  • #6
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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
JasonRox
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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?
 
  • #8
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nevermind , i got it
 
Last edited:
  • #9
HallsofIvy
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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!
 

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