Re: Calculus with double integral xe^(x^2-y^2).

In article <geco8o$lda$1@xxxxxxxxxxxxxxxxxxxxx>,
"mina_world" <mina_world@xxxxxxxxxxx> wrote:

Hello teacher~

Find the value of

int{0 to 1} int{0 to x} x.e^{(x^2) - (y^2)} dydx

+ int{1 to 2} int{x-1 to 1} x.e^{(x^2) - (y^2)} dydx

1) (1/4).(e^3 - e - 2)
2) (1/4).(e^3 - e + 2)
3) (1/2).(e^3 - e - 2)
4) (1/2).(e^3 - e + 2)
5) e^3 - e - 2

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Hm.. Jacobian ?
I need your advice.

This is the double integral of x*e^{(x^2) - (y^2)} over a certain
parallelogram P. What is the simplest linear transformation you know
that takes a square to P? Find that and you'll arrive at a double
integral that can be evaluated. I'm getting 1) for the answer.
.

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