they used a trigonometric substitution,
(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,
Thank you
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!
if you haven't done it in your class, why are you expected to know it for the test?
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 .
Now
plugging this in for in our answer, we find that:
as desired