For a question in stats I need to integrate a function.(Worried)

$\displaystyle \int_0^1(x(ce^{2x})dx)$

I don't know the first thing about integration. So I was hoping for a little help in this part of the question.

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- Sep 25th 2009, 02:24 PMsadmathBasic integration is beyond me...
For a question in stats I need to integrate a function.(Worried)

$\displaystyle \int_0^1(x(ce^{2x})dx)$

I don't know the first thing about integration. So I was hoping for a little help in this part of the question. - Sep 25th 2009, 02:30 PMskeeter
- Sep 25th 2009, 02:41 PMPlato
There is hope for you yet.

Go to this website Wolfram|Alpha

In the input window, type in this exact expression: integrate (c)(x)e^{2x}dx from 0 to 1 (you can copy & paste)

**Click the equals bar at the right-hand end of the input window.**. - Sep 25th 2009, 02:45 PMsadmath
Ok, so I kinda modified the equation now. There is an x in the equation before the ce, but I'll try to figure it out, and you can all feel free to point and laugh at me (Doh)

$\displaystyle \int_0^1xce^{2x} = \left[\frac{cx^2e^{2x}}{2}\right]_0^1 = \frac{c}{2}[e^2-e^0]$

Right? - Sep 25th 2009, 02:47 PMsadmath
@Plato

Sweet I'll check that out. I wonder if it shows how it does it, because it looks like I'll have to get to know this stuff. - Sep 25th 2009, 02:55 PMPlato
- Sep 25th 2009, 03:18 PMsadmath
@Plato:

I tried to remove "from 0 to 1" but I still don't see the "Show steps" button. Maybe I'm doing something wrong? - Sep 25th 2009, 03:26 PMtom@ballooncalculus
Just in case a picture helps...

http://www.ballooncalculus.org/asy/parts/parts.png

... where

http://www.ballooncalculus.org/asy/prod.png

... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. Choosing legs crossed in this case is equivalent to all the stuff about u and v (or f and g) in the integration by parts formula. So fill out the rest of the product-rule shape, and subtract whatever you have to to keep the lower equals sign valid. Then integrate that. So, next step:

http://www.ballooncalculus.org/asy/parts/parts1.png

By the way, integrating $\displaystyle c\ e^{2x}$ means working backwards through the chain rule for differentiation, and therefore having to cancel a multiplication by 2, in order to keep the lower equals sign valid here...

http://www.ballooncalculus.org/asy/intChain/simple.png

... where

http://www.ballooncalculus.org/asy/chain.png

... is the chain rule. Straight continuous lines still differentiate downwards (integrate up) with respect to x, and the straight dashed line does similarly but with respect to the dashed balloon expression (which is the inner function of the composite and hence subject to the chain rule).

__________________________________________

Don't integrate - balloontegrate!

Balloon Calculus Forum

Draw balloons with LaTeX: Balloon Calculus Drawing with LaTeX and Asymptote! - Sep 25th 2009, 04:09 PMmr fantastic
This question should have been asked here: http://www.mathhelpforum.com/math-he...-variance.html

Thread closed. - Sep 25th 2009, 04:20 PMmr fantastic
I suggest ignoring c (it's a multiplying constant and therefore irrelevant to doing the actual integral) and just doing this:

Wolfram|Alpha integral 1

Wolfram|Alpha integral 2

Note the formatting of the input.

Now click Show Steps.