Solved: Integral Question - Finding Average Area Under Curve

[rjs123]

Homework Statement

$$1/2\int_0^2e^{-2x^2}dx$$

I'm basically trying to find the average area under the curve for a rectangle from [0, 2] inclusive...which is why i put the 1/2 in front.

The Attempt at a Solution

I let u = to everything above e
du = -4xdx

$$-1/8x[e^{-2x^2}]dx$$

then plug in 2 ...0...subtract...am i on the right path?

 

[rock.freak667]

There really is no elementary answer for that integral. You will have to use an approximate method in order to evaluate the integral, such as Simpson's Rule or the Trapezium Rule.

 

[Mark44]

Homework Statement

$$1/2\int_0^2e^{-2x^2}dx$$

I'm basically trying to find the average area under the curve for a rectangle from [0, 2] inclusive...which is why i put the 1/2 in front.

The Attempt at a Solution

I let u = to everything above e
du = -4xdx

$$-1/8x[e^{-2x^2}]dx$$

then plug in 2 ...0...subtract...am i on the right path?

In addition to what rock.freak667 said, you attempted to use substitution on this integral, but didn't do it correctly.

In your substitution u = -2x², and du = -4xdx, but you are missing an x factor in your integrand, and there's no way to get it.

 

[dextercioby]

Have a read on the error function http://mathworld.wolfram.com/Erf.html and then you can get the numerical value (erf(2)) from Abramowitz and Stegun's book.