Question

how to intargrate e^-x^2

Answer 1

you can expand the exponential using power series to get a function.

Answer 2

Or you can use get it into another dimension as well.

\[\iint_R e^\left\{ -x^2-y^2 \right\}d\]

Answer 3

@Spacelimbus is right, you can also do that! Convert it to polar coordinates, I think.

Answer 4

sorry, the equation editor messed up for me, it should be dydx

Answer 5

\[\iint_R e ^\left\{ -x^2-y^2 \right\}dxdy\]

Answer 6

And from there, as @abb0t mentioned, get it into polar coordinates.

Answer 7

thanks guys i already tryied by parts

Answer 8

\[\iint_R r e^ \left\{ -r^2 \right\}drd \theta\]

Answer 9

Do you know how to go from here @Rhandzu ?

Answer 10

@Spacelimbus , no can you please help me step-by-step

Answer 11

convert to polar from where spacelimbus pointed out up there \(r^2 = x^2+y^2\)

and don'4 forget about the jacobian

Answer 12

You should get: \[\int\limits_{0}^{2\pi}\int\limits_{0}^{\infty} re^{-r^2}drd \theta\]

Answer 13

NOW you can use u-substitution.

Answer 14

\[\checkmark\]

Answer 15

Which i am sure you can easily finish the problem from here.

Answer 16

thank you guys

Answer 17

i'm new to culculas but i do have math basics

Answer 18

@Spacelimbus , can you please tell me the name of that formula

Answer 19

Hmm good question actually, it's a technique I have once seen, I guess it's a "Double improper integral method", Dirichlet Integrals use similar methods to be evaluated. Let me see, this might help you as well:

http://www.youtube.com/watch?v=fWOGfzC3IeY

As seen on MIT in their Multivariable Calculus Courses.

Answer 20

wow thanks great Video, so do i use the same method to integrate sin(x^2)

Answer 21

no, for sin(x^2) the easiest would be to use a maclaurin series representative, the method worked above because of the exponential laws, with the trigonometric functions that wont work so easily.

Answer 22

I would approach that one by using taylor series, but I think you can probably do the same.

Answer 23

@abb0t tell me more

Answer 24

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