Recent content by rdioface

facepalm.jpg Thanks!

Yes, the problem asks to verify that y(t) is a solution to the differential equation y' + 4ty = 1.

Homework Statement For the differential equation, verify (by differentiation and substitution) that the given function y(t) is a solution.Homework Equations y' - 4ty = 1 y(t) = \int_{0}^{t} e^{-2(s^{2}-t^{2})} ds The Attempt at a Solution I attempted to take \frac{d}{dt} of y(t) as usual...

Help with Gaussian integration problem please :) Homework Statement Compute the improper integral \int^{\infty}_{-\infty}x^{2}e^{-x^2}dx given \int^{\infty}_{-\infty}e^{-x^2}dx=\sqrt{\pi}. Homework Equations Just the rule for doubly-improper integrals I guess...

Homework Statement Prove the convergence or divergence of the series \Sigma(\frac{n}{2n+3})^{2} using the Direct Comparison Test. Homework Equations If series A converges and every term in series B is less than the corresponding term in series A, then series B converges. If series C...

Danke schoen!

Homework Statement Find the integral of cot^6(x) without using the reduction formula. Homework Equations Potentially any trig identities involving the cotangent The Attempt at a Solution I tried splitting up the cot^6 in various ways such as cot^4*cot^2 and cot^2*cot^2*cot*2 but...

Homework Statement Find the area of the lemniscate r2=6cos(2w) located to the right of the line r=3/2sec(w). Homework Equations Area of a polar region is the integral from a to b (in this case a and b are where the curve intersects the line, I believe) of 1/2*r2d(w). The Attempt at...

Alright thanks, it seemed like there might have been some crazy trig identity I was missing or something.

That gets me to r^2(4 + 5sin^2(t))=36. Are there any further steps to be done?

Homework Statement Convert the following Cartesian equation to polar form. x^2/9 + y^2/4 = 1 Homework Equations r*cos(t)=x r*sin(t)=y r=Sqrt(x^2 + y^2) y/x = Arctan(t) The Attempt at a Solution I get ugly looking things like r^2(cos^2(t)/9 + sin^2(t)/4) = 1 but being a simple ellipse (edit...