Thanks ryos.

]]>Edit: on the plus side, this post made me finally learn LaTeX, or at least enough to write it.

[Please ignore this post as it is made of 100% pure stupidity. x_x]

]]>As to where I got it, umm...read my posts again.

]]>(3e³ - 2e²) - (e² - e²)

What the math? Where did you come up with that? It should be 3e^3 - e^3 - (2e^2 - e^2). Where the heck did you come up with such a visually repelling expression?

Well I'm just about finishing calculus now. So I'll probably be getting into calculus 2 soon.

]]>Anyway mikau, my question (which both you and irspow answered the same way) is this, using your example:

xe^x - e^x

Is it:

(3e³ - 2e²) - (e³ - e²)

...or is it:

(3e³ - e³) - (2e² - e²)

...? Actually, working through the two, they both come out the same. Is this always the case, though? Let's see:

Let h(x) = uv and g(x) = ∫u′v, then assert:

[h(b) - h(a)] - [g(b) - g(a)] = [h(b) - g(b)] - [h(a) - g(a)]

h(b) - h(a) - g(b) + g(a) = h(b) - g(b) - h(a) + g(a)

So it is. Ok, dumb question. *smacks self*

Edit: on the plus side, this post made me finally learn LaTeX, or at least enough to write it.

]]>But if I am...

Evaluating a definite integral that requires integration by parts?

As far as I know, you simple use u and V as substitutions for the variable of integration, when your done you replace it with its original value.

For instance ∫ x e^x dx from x = 2 to x = 3

This is probably the easiest integration by parts problem. Let u = x, du = dx. Let dV = e^x dx V = e^x

so we use the formula ∫ u Dv dx = uv - ∫ V du

insert the values back in and we get:

x e^x - ∫ e^x dx

= x e^x - e^x

= e^x( x - 1)

Now we evaluate this from x = 2 to x = 3:

2e^3 - e^2

piece of cake.

]]>There was an error in it though, which I've now corrected.

]]>Here's one that should be more clear:

From this, it should be clear that you must first divide up your function into two parts, u and dv, then solve for v and du, and finally just plug it all back in.

]]>[h(b) - h(a)] - [g(b) - g(a)]

]]>When actually evaluating the integral, I'm not sure how to interpret this. I think it could be either:

...or, it could be:

Is it one of those, or something else entirely?

(Good gads, LaTeX competes with regular expressions for ugliest mishmash of punctuation ever.)

]]>