Change of variables Definition and 219 Threads

define L[u] = a \frac{\partial^2u}{\partial t^2} + B \frac{\partial^2 u}{\partial x \partial t} + C \frac{\partial^2u}{\partial x^2} = 0 show that if L[u] is hyperbolic then and A is not zero the transofmartion to moving coordinates x' = x - \frac{B}{2A} t t' = t tkaes L into a...

Hmm, I can't seem to get this double integral transformation: int(limits of integration are 0 to 3) int (limits of int are 0 to x) of (dy dx)/(x^2 + y^2)^(1/2) and i need to switch it to polar coordinates and then evaluate the polar double integral. i sketched the region over which i am...

Hi, I'm having trouble understanding the solution to a question from my book. I think it's got something to do with the chain rule. The problem is to prove the change of variables formula for a double integral for the case f(x,y) = 1 using Green's theorem. \int\limits_{}^{} {\int\limits_R^{}...

Hi, I'm having trouble evaluating the following integral. \int\limits_{}^{} {\int\limits_R^{} {\cos \left( {\frac{{y - x}}{{y + x}}} \right)} } dA Where R is the trapezoidal region with vertices (1,0), (2,0), (0,2) and (0,1). I a drew a diagram and found that R is the region bounded...

let f be continuous on [0,1] and R be a triangular region with vertices (0,0), (1,0) and (0,1). Show: the double integral over the region R of f(x+y)dxdy = the integral from 0 to 1 over u f(u)du I recognize it is a change of variables problem but I'll be damned if I can create a set of...

I asked this in another thread, but I think this forum might be a better place for it (not trying to spam the same question). When deriving the formula for relativistic kinetic energy, we start with KE = \int_{0}^{s} \frac{d(mv)}{dt} ds = \int_{0}^{mv} v d(mv) So I figure that since v =...

Which change of variable should I use to find: \int\int_D (x^4-y^4) dxdy Where D is in the first quadrant with" 1 \leq x^2-y^2 \leq 3, 2\leq xy \leq 3

let be the integral: \int_1^{\infty}\int_{-\infty}^{\infty}f(x,y)dydx i make the change of variable xy=u y=v whose Jacobian is 1/v but then what would be the new limits?...

Hi, I'm not sure how to do this question. Any help would be great. Let B be the region in the first quadrant of R^2 bounded by xy=1, xy=3, x^2-y^2=1, x^2-y^2=4. Find \int_B(x^2+y^2) using the substitution u=x^2-y^2, v=xy. . Use the Inverse Function theorem rather than solving for x...

Hi I'm having trouble with using change of variables. \int\limits_{}^{} {\int\limits_R^{} {f(x,y)dA = \int\limits_{}^{} {\int\limits_{}^{} {f(x(u,v),y(u,v))\left| {\frac{{\partial \left( {x,y} \right)}}{{\partial \left( {u,v} \right)}}} \right|dudv} } } } I've got two examples to...

Hi. I have a problem with a question. Basically, I have an integral that goes from x=0 to x=1, and I'm supposed to make a change of variables like this: Let x = 1 - y^2. The problem I'm having is trying to find the limits of integration after the change of variables. Since y = +/-...

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 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 Now I know polar coordinates would be the most efficient way, and thus I could say r= \sqrt{x^2 + y^2} . Is this legal to use polar coordinates...

Can anyone give me any hints as to find a suitable change of variables for this integral. infinity / |dt/(a^2+t^2)^3/2 = | / -infinity =2/a^2 * integral below...

Let R be the region bounded by the graphs of x+y=1, x+y=2, 2x-3y=2, and 2x-3y+5. Use the change of variables: x=1/5(3u+v) y=1/5(2u-v) to evaluate the integral: \iint(2x-3y)\,dA I found the jachobian to be -1/5 and the limits of integration to be 1<=u<=2 2<=v<=5 so i set up...

Ok, i have a problem with this double integral. I am having a hard time finding the limits. The question is Evaluate \iint \frac{dx\,dy}{\sqrt{1+x+2y}}\ D = [0,1] x [0,1], by setting T(u,v) = (u, v/2) and evaluating the integral over D*, where T(D*)=D Can some one help me find the...

Does anyone know of any sources that explain change of variables for double integrals. Actually, I get the change of variables thing, but a few of our problems don't give us the transforms. I don't understand how to create these myself. Here is an example: Math Problem So far, I found...

Wacky change of variables for Multi integration! Arghh I am having diffiiculty with these problems. I am having difficulty mastering the LaTeX form--- (things like how to make a double integral etc) so if you look at this site...

im working on these, and I am supposed to find the image of a set under a given transformation. can someone please explain to me a good way of doing this?