[SOLVED] Double integral with cos(x^n) term
Homework Statement
Solve the following integral (without using a series development):
\displaystyle
\int _{0}^{\frac{1}{8}}\int _{\sqrt[3]{y}}^{\frac{1}{2}}\cos\left(20{\pi}x}} ^{4}\right)dx dy
Homework Equations
N/A
The Attempt at a...
Hello,
Although I recently had a MATLAB class it didn't really touch on variable types or use of the solve() function, and now I'm stumped on an embarrassingly basic problem; I'm trying to solve an equation in this form, with the other variables defined as doubles...
[SOLVED] Parametric equation of the intersection between surfaces
Homework Statement
Given the following surfaces:
S: z = x^2 + y^2
T: z = 1 - y^2
Find a parametric equation of the curve representing the intersection of S and T.
Homework Equations
N/A
The Attempt at a Solution
The...
Oh, right, I just didn't think of assuming a unit sphere centered at the origin - much easier now. And yeah, the curve just follows a spherical surface.
Thanks-
Given a curve described by the following function:
r(t) = (cos^2(t), sin(t), sin(t)*cos(t)), 0 ≤ t ≤ 2*Pi
How can I prove it describes a spherical shape? I know that the parametric representation is the following, but I'm not sure how to reconcile that with the expression of a sphere.
x =...