Basically need help with this, probably something really retarrded by me, if someone couuld point out where I went wrong/how to do it right would be cool.
Re: Integration question I got wrong and idk why :(
Forget the image or create a better one that is crystal clear because this is not very good (hold camera lens parallel to page or even put in a window that has plenty of light or illuminate it with a lamp and FOCUS! lol )
In any case just type in characters what your integrating function and limits are in a plain post or what the problem is about and try the homework session in the future.
Re: Integration question I got wrong and idk why :(
Ummm -- I took a quick look. It was a pretty obvious mistake, so here goes...
I[f(x)] means the indefinite integral of f(x). D[f(x)] means the derivative of f(x).
Ok, so you want to find:
I[(e^(2x) - 2)^2]
Here's basically the way you reasoned through this, I think:
You saw this:
Let D[blah] = D[(e^(2x) - 2)^3]
Then:
D[blah] = 3*(e^(2x) - 2)^2 * 2 * e^(2x)
D[blah] = [6 * e^(2x)] * [(e^(2x) - 2)^2]
You basically realized that the bold terms match, so you just divided [blah] by [6*e^(2x)], hoping this would give you the integral you're looking for. But you didn't account for the fact that when you take the derivative of [blah]/[6*e^(2x)], you have to use the product/quotient rule and differentiate both parts of the product/quotient. In other words, you can't do this kind of thing unless you get a constant coefficient (you got a coefficient in terms of 'x' instead).
You could probably do this using integration by parts, but it's easiest just to distribute out the term you're trying to integrate first:
I[(e^(2x) - 2)^2] = I[e^(4x) - 4e^(2x) + 4]
The right hand side should be pretty easy to deal with...
Re: Integration question I got wrong and idk why :(
Quote:
Originally Posted by pocketzeroes
Ummm -- I took a quick look. It was a pretty obvious mistake, so here goes...
I[f(x)] means the indefinite integral of f(x). D[f(x)] means the derivative of f(x).
Ok, so you want to find:
I[(e^(2x) - 2)^2]
Here's basically the way you reasoned through this, I think:
You saw this:
Let D[blah] = D[(e^(2x) - 2)^3]
Then:
D[blah] = 3*(e^(2x) - 2)^2 * 2 * e^(2x)
D[blah] = [6 * e^(2x)] * [(e^(2x) - 2)^2]
You basically realized that the bold terms match, so you just divided [blah] by [6*e^(2x)], hoping this would give you the integral you're looking for. But you didn't account for the fact that when you take the derivative of [blah]/[6*e^(2x)], you have to use the product/quotient rule and differentiate both parts of the product/quotient. In other words, you can't do this kind of thing unless you get a constant coefficient (you got a coefficient in terms of 'x' instead).
You could probably do this using integration by parts, but it's easiest just to distribute out the term you're trying to integrate first:
I[(e^(2x) - 2)^2] = I[e^(4x) - 4e^(2x) + 4]
The right hand side should be pretty easy to deal with...
Cheers man yeah that is exaclty what I did, completely forgot that i would have to differentiate the 6*e^2x.
And yeah does work out fine doing it the easier way, thanks a bunch.
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