Recent content by silicon_hobo

bump (save me from these numbers and symbols)

Sorry, I've made this really confusing (for myself as well). When i put the integration of sec^3 in latex i used x but if you look to the top it should actually be an integration of sec^3 theta which is the result of a substitution of -sin x for tan theta.

Ok, so is that a yes or no to the "do I need to change the limits of integration a second time" question:P Thanks for your patience folks. It's a rotation about the x-axis.

Right, but do I have to change the limits of integration again for the 2nd sub to tan & sec^2... seems like I have done this one the hard way.

Thanks for the reply. Alright so if I inetgrate the first one fully from sec^3 I get: \int^\frac{\pi}{3}_{0}(sec^3\ x\ dx) = sec\ x\ tan x - \int(sec\ x\ tan^2\ x dx) = sec\ x\ tan\ x - \int(sec\ x\ (sec^2\ x - 1) dx) = sec\ x\ tan\ x - \int(sec^3\ x\ dx) + \int(sec\ x\ dx) = sec\ x\...

Homework Statement I'm not sure how to proceed here. The first one asks me to find the area of a surface obtained by rotating the curve y = cos(x), 0 \leq x \leq\ \frac{\pi}{3} The second one asks to Solve: \frac{dy}{dt} = \frac{ty+3t}{t^2+1}\ y(2)=2 Homework Equations The Attempt at...

Wow, that seems almost too easy. Thanks.

[SOLVED] Separable Equation with Condition? Homework Statement Solve. http://www.mcp-server.com/~lush/shillmud/int3.71.JPG Homework Equations The Attempt at a Solution I'm not sure how to separate this. Also, since the directions consist of only one word, I'm not sure if y(2)=2 is...

Homework Statement Identify and sketch the curve represented by the parametric equations: x=1+cost y=1+sin^2t Homework Equations The Attempt at a Solution I have to isolate t in one of these equations and sub whatever t equals into the other equation right? So how do I get rid of the...

Homework Statement a)Prove the reduction formula: \int\ tan^n\ x\ dx\ =\ \frac{1}{n-1}tan^{n-1}\ x\ -\int\ tan^{n-2}\ x\ dx Hint: first write tan^n x as tan^{n-2} \ x\ tan^2\ x and the rewrite using tan^2\ x+1=sec^2\ x. b) Use the formula twice to find \int\ tan^4\ dx The Attempt...

Homework Statement Determine whether each integral is convergent or divergent, if convergent find its value. a) \int^2_1 \frac{dx}{x \ ln \ x} b) \int^3_0 (\frac{1}{\sqrt{x}})e^{-\sqrt{x}}\ dx The Attempt at a Solution Hey Folks, I'm still at it. Both of these integrals have...

Homework Statement \int xe^{2x^2} cos(3x^2) dx This is the hardest integral I've attempted so far. I've come up with an answer that fits a table in my book but I'm not sure if I arrived there correctly. Thanks for reading! Homework Equations \int e^{au} cos\ bu\ du\ =...

Okay, I think we agree on the first one: http://www.mcp-server.com/~lush/shillmud/int2.4a2.JPG But how do I get rid of that pesky d\theta? This is what I've got so far for #2. I'm not sure if I've applied the identity correctly: http://www.mcp-server.com/~lush/shillmud/int2.4b.JPG

Homework Statement Hey, it's me again. This method is giving me some trouble. This is the first problem: \int^3_0\ x^2\sqrt{9-x^2} \ dx The second problem is: \int\frac{dx}{\sqrt{2x^2+2x+5}}. How do I use a trig. substitution to start on this one? Homework Equations The Attempt at a...

Okay, I've transformed the limits while using 'u' in the top image. Does that work?