1. Evaluate .

2. Evaluate

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I know I need to use substitutions in both cases but I'm not sure what to substitute so it works out nice... I've tried a few things like for the first one but I couldn't get to work out...

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- December 3rd 2007, 09:22 PMebonyscytheSolving an integral by substitution (two questions)
1. Evaluate .

2. Evaluate

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I know I need to use substitutions in both cases but I'm not sure what to substitute so it works out nice... I've tried a few things like for the first one but I couldn't get to work out... - December 3rd 2007, 09:47 PMJhevon
- December 3rd 2007, 09:58 PMDivideBy0
What is the effect of the absolute value signs in the second question? (Thinking)

- December 3rd 2007, 10:23 PMebonyscythe
Thanks much... I got the first question just fine after that, but when I try to use u=cos(x), then wouldn't du=-sin(x)dx? I'm having a tough time with the absolute value.

My train of thought for the second one... where am I going wrong?

Which I know is wrong because I got 4/3 from Derive... - December 3rd 2007, 10:34 PMJhevon
- December 3rd 2007, 10:50 PMebonyscythe
How would I know to split the interval at pi? Maybe it's because it's two in the morning but this problem is giving me some real trouble... so if I split the interval and substitute... would I get

? - December 3rd 2007, 10:53 PMJhevon
the absolute values turns the function positive when it is negative. thus you must find the interval on which the function is negative, and integrate the negative of the function (which will be positive) over that interval. graphing is the easiest way to see where it is negative, and it is negative on pi to 2pi in that interval

- December 3rd 2007, 11:00 PMebonyscythe
Ah, okay... I was thinking for some reason that I wanted the interval of which cos(x) is negative instead of the whole function cos(x)^2sin(x)... dumb mistake made, thanks for explaining.

Anyways, not sure if you're getting to it but am I heading in the right direction for the substitution? - December 3rd 2007, 11:01 PMJhevon
- December 3rd 2007, 11:13 PMebonyscythe

Let u = cos(x) so du = -sin(x) dx

*need a -1 in the first integrand to substitute, so multiply by a factor of one

substituting, I get...

I'm trying to make sense of what I've got in my notes, so I've no idea where to go next or what I'm doing wrong here... - December 3rd 2007, 11:25 PMJhevon
- December 3rd 2007, 11:30 PMebonyscythe
Ah crud, it's u^2, not cos(x)*u... right? That would make more sense... So...

Let u = cos(x) so du = -sin(x) dx

- December 4th 2007, 12:01 AMangel.white
Also, a friendly warning.

looks like

which is not the same as

:)

I had a test where I had to differentiate:

And I interpreted the exponent 3/5 as being applied to the entire natural log, rather than to the inside of the natural log. Cost me 2.5% of my total test grade -.- - December 4th 2007, 11:04 AMJhevon
You are correct. I was going to make a similar comment last night...don't know why i didn't. i'm getting too old.

Quote:

And I interpreted the exponent 3/5 as being applied to the entire natural log, rather than to the inside of the natural log. Cost me 2.5% of my total test grade -.-

- December 4th 2007, 11:22 AMangel.white
:) I got 74/80 = 92.5%

Also lost a point for incorrectly transcribing a correct answer, explaining in a paragraph why one of the limit questions must be equal to zero rather than manipulating it to be equal to zero, and 2 points for forgetting the very last link in a chain rule differentiation.

But then my instructor curved it, so the grade on the books is out of 74 ;)