I'm tutoring someone in Calc I over the summer and she came to me with the following two problems on a pre-test. It's been awhile since I've done u-substition, and I think I've got it right, but don't want to set her on the wrong track. The problems:
1) (integral of) ((ln(rt(x))) / x )dx
2) (integral from -8 to 0) (1 / (rt(1-x)))dx
I didn't get much out of the first, but the second, I found it to be -2 + 2(rt(-7)). Would someone be able to verify this result, as well as assist with the first problem?
Thanks in advance!
Ah- thank you for the correction on the second problem. That was rather short-sighted of me. @_@
As for the first problem, I got that far- but I couldn't remember how to proceed with any degree of certainty. Unfortunately, she doesn't have the answer, as it's a "pre-test" problem. What would be the next step moving forward from "u" and "du"?
Aside- thanks for the bracket thingy. I forgot that you could do stuff like that on forums.
That was actually my difficulty- because the problem has , I wasn't sure if could be pulled outside the integral (or something to that effect), which would then leave the proper dx substitution of .
Like I said, I got as far as figuring out what the substitution was supposed to be ( , ). As far as actually implementing the substitution, it's been awhile since I've done u-sub (much to my chagrin), and I want to get this right for my student- especially as it's a pre-test problem. If I had the next step, I could probably take the problem from there- it's just the next step that's killing me.