# Double integration of an exp function

• Vandella
In summary, the person was trying to integrate e^(-x^2) dydx but was struggling and needed help. They tried integrating with respect to y but got an error function and then tried integration by substitution but wasn't sure if it would work. They then tried integrating x^2 and possibly got the answer.
Vandella

## Homework Statement

Please help I need to find the area of e^(-x^2) with the domain 0 is less than or equal to y which is less than or equal to 1 and y is less than or equal to x which is less than or equal to one

## The Attempt at a Solution

I set up the equation ∫ ∫ e^(-x^2) dydx with values y=x and y=0 and x=1 and x=0
attempted to integrate but struggling.

Let's see your attempt at integration then

Well I started by integrating with respect to y and got ye^(-x^2)dx,I then solved for the values y=x and y=0 leaving xe^(-x^2)dx and unsure of if my first steps are correct and how to continue.
My idea for a next step would be integration by substitution u=-x^2 but unsure as to whether that would work

why -x^2?
I'd just go for x^2

Try it and see what happens

Ok here goes u= x^2 that gives ∫ e^(-u) integration by substitution gives me -(e^x^2)/2
Possibly :)

Now do I just solve for x=1 and x=y?

When you did your first integration, you essentially integrated the strip from 0 to y=x, in the second integration you are taking all of those strips from 0 to 1, you don't need to solve for x=1 or x=y, you just need to evaluate the integral from 0 to 1

Sorry when I said solve I meant evaluate.
Could I switch the order of integration so when I evaluate after integrating a second time I lose x and y from the equation?

Try it and see what happens
You'll have trouble evaluating it if you do the dx integration first however, the integral of e^(-x^2)dx isn't nice, it isn't solvable in terms of elementary functions. If you're interested, the name of the solution is the error function.

Thanks for your help will just leave it now and not confuse myself even more

Vandella said:
Thanks for your help will just leave it now and not confuse myself even more

The best way to get use to it is to just play about with it and see what you end up with.

## What is double integration of an exp function?

Double integration of an exp function is a mathematical process of finding the integral of an exponential function twice. It involves finding the area under the curve of the exponential function with respect to two different variables.

## Why is double integration of an exp function important?

Double integration of an exp function is important because it is used in many areas of science and engineering to model various processes and phenomena. It allows for the calculation of important quantities such as work, displacement, and velocity.

## What is the process for double integration of an exp function?

The process for double integration of an exp function involves finding the integral of the function with respect to the first variable, and then finding the integral of the resulting function with respect to the second variable. This is usually done using the rules of integration and substitution.

## What are the limitations of double integration of an exp function?

One limitation of double integration of an exp function is that it can only be used for functions that can be expressed as an exponential function. Additionally, the process can become complex and time-consuming for more complicated functions.

## How is double integration of an exp function different from single integration?

Double integration of an exp function involves finding the integral of a function twice, while single integration only involves finding the integral once. Double integration is often used to calculate more complex quantities, while single integration is used for simpler calculations.

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