I kinda had an itch the antiderivates weren't that easy to compute :( Now I only have 20 minutes left... :( He said we could use a calculator to compute the integrals instead of doing all the computation by hand, but unfortunately I have a very outdated ti-85 and not one of those new shiny...
Wow, that was an excellent explanation. I can't thank you enough! :)
However, the abtiderivative of csc^3\theta is csc\theta(cot^2\theta +1) (if I'm correct) for t goes from pi/4 to pi/2, isn't cot^3\theta undefined for theta = pi/2 ? Since the cotangent is just 1/tan...and...
OK, I'm an idiot. I forgot my math book and I don't have the formula for integrals regarding csc and sec for powers larger than 2...could you please help?
I'm trying to take the integrals of \csc^3\theta d\theta and \sec^3\theta d\theta
I'm kinda in a rush as I need to turn this...
I'm sort of confused...I thought the Jacobian was a matrix computation of derivatives, and that rdrd\theta was simply a representation of dA, or are the two synonamous? I mean, would I be able to show that the jacobian is rdrd\theta through a derivative matrix?
thanks again!
Thank you SO much hypermorphism! Wow, you seem to have this stuff down pat. Impressive! I'm still a bit lost as to the orientation of the triangles...are you drawing the triangle from (0,0) to (1,1) and splitting the box that way...or what orientation are you splitting it from? I'm just...
Sorry, I'm being hardheaded. :( I'm just getting these conflicting reports that it wouldn't be 'that hard' to convert to polar coordinates, and now I hear it can't be done at all. So does that mean my original method setting u=x^2 and v=y^2 is the most efficient way? Or are there alternative(s)?
Thanks very much hypermorphism, and THANKS for catching my fatal flaw with the Jacobian computation...wow was I ever off. I'm just completely lost at this point. I don't really know what you mean by splitting the square into two triangles...I mean I literally know what you're talking about but...
I'm totally at a loss here guys. I realized my Jacobian was computed wrong. Can someone please give me a clue as to what would be the most efficient integral setup? I'm completely dumbfounded. :( Thanks
edit: more in-depth post in the calculus forum, thanks
Is there any easy way to determine this? I'm assuming the interesection is symmetrical, since the pyramid has length 8 on all sides and the cylinder is uniform. Though I could be wrong...
Thanks very much HallsofIvy for your reply. I would have simply integrated with respect to x and y, but I specifically have to integrate using change of variables. I did so, as I mentioned above, by doing the following:
I set u = x^2, v =y^2, and then calculated the jacobian of T which was...
Thanks much Daniel, greatly appreciated. I assumed it was a cylinder because the problem specifically stated it is a cylinder, so I used cylindrical coordinates accordingly since I thought that'd be the best way to go about it. I graphed the whole thing and I understand that the xy plane and...
I'm trying to evaluate the double integral
\int \int \sqrt{x^2 + y^2} \, dA
over the region R = [0,1] x [0,1]
using change of variables.
Well, after fooling around, I've got an answer. I set u = x^2, v =y^2, and then calculated the jacobian of T which was 1. The image transformation...
I'm supposed to find the volume of the solid bounded by the cylinder x^2+ y^2 =25, the plane x + y + z =8 and the xy plane.
So I decided to use cylindrical coordinates, in which E is bounded by the cylinder r=5, the plane z = 8 - y -z = 8 - r cos(theta) - r sin(theta) , and theta goes from 0...
lol dang...must be a slow day around here? :(
Well, after fooling around, I've got an answer. I set u = x^2, v =y^2, and then calculated the jacobian of T which was 1. The image transformation limits of integration for u and v turned out to be the same [0,1] x [0,1]
So I did the...