I've been trying to solve this problem for a while now and getting no where.

Problem: Evaluate (leave in rectangular coordinates):

∫ [-1, 1] ∫[-√(1-x^2), √(1-x^2)] ∫[-√(1-x^2-y^2), √(1-x^2-y^2)] dz dy dx

I get up to here, before everything becomes a bit crazy;
∫ [-1, 1] ∫[-√(1-x^2), √(1-x^2)] 2√(1-x^2-y^2) dy dx

I'd really appreciate if anyone could ( Read more... )

( Please check my calculus! I'm making a model of a solid with well-known cross sections... )

I am having trouble finding my limits of integration. First of all, I am trying to find the volume of a solid that has the cross sections in the shape of equilateral triangles of a function.
My equation is x2 + y2 = e2, so on a graph it would make a circle shape, right?
I will find the volume by finding the integral of the equation of the area of ( Read more... )

My physical chemistry class has turned into a math class, and it's been a few too many years since I've taken calculus for me to be sure of myself.

Here's what I'm trying to integrate followed by the solution given by the Mathematica Online Integrator.


( Read more... )

Integrate: 1/(x^7 + x) using u substitution.

So, the denominator could be restated as x(x^3)^2 + x  with u=x^3...except that du would have to equal 3x^2 and I'm not sure how that would work. Am I on the right track?