Flemish

Do you have any analytical method for this?

This equation is true for a rocket: where, m is mass, v is velocity, g is 9.81, k is constant, u is the velocity at which mass is being ejected and gamma is the rate at which mass is being ejected. I have drawn up two methods, the Euler's method and perturbation theory. I need a third method and can't seem to think of any. All suggests would be great.

Alright, I'll try that next time! Ah, that makes a whole lot of sense. The reason why it was such a long process was because I was trying to find the transformation and Jacobian. I had to find all the lines that would make the parallelogram and then find the shape that it transform into. Also had to find the Jacobian. In the end of the day, two of the lines ended up equal something like 4=0 which made no sense meaning I was unable to find the new shape. Thank you, have you been very useful!

So in this case what would make a good substitution and why? Also what do you mean my linearly independent variable?

Thank you sir! I understand where your coming from. Sorry my brain wasn't working before.

I have recently been studying double integrals. One of the topics were double variable substitutions. I find it hard to find the right double variable substitutions. For example: I substituted y = 1/2(u+v) and x = u+v, in hopes of getting rid of (2y-x)^3/2 and making the integral easier. However, this led me down a very long process and ended up being too complicated for it to work. Any advice?

what is wrong with it, I double checked

That wouldn't fix the problem because the inside the square root will still be zero

Sorry, I meant from a to -a Sir, I don't get what you mean by start with b^2 = a^2- x^2, are you referring to the limits or a substitution? If its a substitution then how would it fix our problem? If your talking about the limits, here is how I got them: My logic is that because its a circle, the y-values have to be given by this.

Hello, I have been stuck on this Math problem and wanted some help. This is the formula for finding out the surface area: Using this formula, you should arrive on something like this (the outer limits are pi/4 and 0, the program didn't let me input). Focusing on the inner integral, by rearranging you arrive on this If you integrate this, the answer will always be zero: The answer to this always has to be zero, because inputting the limits inside the square root would give zero. However, if you switched to polar coordinates, you'd arrive on a different answer: Which would give you an answer of 2(pi)(a^2). I searched around and people were saying that answers mean different things in different coordinate systems. I understand this, but if region R is a constant area throughout the different coordinate systems, then an answer of zero in the cartesian plane would suggest that the surface area is zero. Meaning that R hasn't have any surface area (assuming R is a constant area through coordinate systems), then no matter the coordinate system, the answer should be the same. Where did I go wrong?