(remember, we treat x as a constant throughout the entire problem)
can you do the integral now that you know that?
to make the math symbols "look nice," we use LaTex
I'm sorry in advance that I don't know how to make this look nice like the other posts do.
I have this integral $ xdy/(x^2 + y^2)^(3/2) where x is a constant.
The answer is given to me as y/x(x^2 + y^2)^(1/2)
I am able to work backwards by taking the derivative of the answer to get the original integral but I can't figure out how to work the integral.
Any help would be appreciated,
I still can't do the integral but atleast I know where to start looking. I have my math book open to the Trigonometric Substitutions chapter now. I'm taking Physics II and Calc II this semester and this is actually part of a physics problem I have involving electric fields. It looks like I'm 2 to 3 weeks away from learning the Trig Substitution method in my Calc II class. I worked through this physics problem and I got the integral set up but then I couldn't figure out what to do with the part of it that I just posted.
I've been going around and around with this problem now for hours. I thought that I must know how to work that integral but I just couldn't figure it out. I have a test in the morning so I need to get this figured out tonight...if I don't pass out first. I'm exhausted.
Thanks for your help!
Let ....remember this, we will get back to it
So our integral becomes:
now we have an answer in terms of , but we want an answer in terms of y
now recall that we said
so if we draw a right triangle with an acute angle , the side opposite to the angle will be and the side adjacent the angle will be . By Pythagoras, the hypotenuse will be .
plugging this in for in our answer, we find that: