Thread: Basic integration is beyond me...

1. Basic integration is beyond me...

For a question in stats I need to integrate a function.

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

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

For a question in stats I need to integrate a function.

$Integrate(From 0 to 1) (ce^(2x)dx)$

I don't know the first thing about integration. So I was hoping for a little help in this part of the question.
$\int_0^1 ce^{2x} \, dx = \left[\frac{c}{2}e^{2x}\right]_0^1 = \frac{c}{2}[e^2 - e^0]$

For a question in stats I need to integrate a function.

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

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

4. 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

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

Right?

5. @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.

@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.
Yes it does.
But you must make an indefinite integral: remove "from 0 to 1".
There will be a 'show steps' buttom.

The point is, this is a resource you can use without all the basics.

7. @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?

8. Just in case a picture helps...

... where

... 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:

By the way, integrating $c\ e^{2x}$ 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...

... where

... 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!

For a question in stats I need to integrate a function.

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

I don't know the first thing about integration. So I was hoping for a little help in this part of the question.
This question should have been asked here: http://www.mathhelpforum.com/math-he...-variance.html

@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?
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.