Homework Statement
Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perp. to the rod.
Homework Equations
integral form of Gauss's law wrt gravitation
The Attempt at a Solution
Can I use...
Ah of course, 0 to 2 will be my x bounds. Thank you for the time you took to make the diagram. I see my mistake before. I redrew it with help from your picture and it is clear that my lower bound is x=0.
Thank you for the reply, Jack, in my drawing I see that my bound for x would start at x=2. I want to say my lower bound is x=-2 because of where z=-x crosses x=2-y^2. Is that right?
Homework Statement
Hi guys, I need help setting up an integral.
Problem: Compute the integral f(x,y,z)=xyz over the solid region bounded below by plane z=-x, above by z=x, and otherwise b the parabolic cylinder x=2-y^2
This is not a surface integral, is it? Because the problems...
Homework Statement
In our lab recently we measured the resistance of copper as a function of length. I plotted a graph with resistance as the dependent variable and length/area as the independent variable. I know the slope of the best fit line is equal to the resistivity of copper and that...
Probably not one book, but you can follow the standard curriculum set in a uni:
First would be a calculus book, like Stewart's.
Second maybe Boas' Mathematical Methods in the Physical Sciences. I think the second edition you can get super cheap.
Anything you don't understand in Boas you can...
Homework Statement
Find the real and imaginary part of sin(4+3i)
Homework Equations
sinx = \frac{e^z - e^(-z)}{2i}
cosx = \frac{e^z + e^(-z)}{2}
sin(iy) = i\frac{e^y - e^(-y)}{2}
cos(iy) = \frac{e^y + e^(-y)}{2}
various trig identities
The Attempt at a Solution
So I used sin(x+y) trig...
Homework Statement
Use special comparison test to find if \frac{2+(-1)^n}{n^2+7} is convergent or divergent.Homework Equations
Special comparison test using the convergent series \frac{1}{n^2}
and taking the limit as n-> infinity of my initial series \frac{2+(-1)^n}{n^2+7} divided by my...
so I got du = (e^x)/3 dx. What do I do with this expression? I thought I was supposed to solve for dx, and plug that into my integral with my u's. Is that not right?
integral: 3u / (9u^2 + 9) * 3 / (e^x) du