Question

What is the integral of ln(x+1) on (1,2)?

Answer 1

Use int by parts

Answer 2

is that the correct integral?\[\int\limits_{1}^{2} \ln(x+1) dx\]

Answer 3

I tried, but it still didn't come out correctly... I also tried making u=x+1 and then using int by parts, but the answer the lesson gave me was also different (xln(x+1) - x + ln(x+1) on (1,2)). lol so i have no idea how they got that

Answer 4

yes, that's the right integral :)

Answer 5

\[\int\limits \ln (x+1) \, dx\]
u=x+1
du=dx
-------------------------------------------------------------
\[\int\limits \ln u \, du\]
Int by parts
\[\int\limits f \, dg=f g-\int\limits g \, df\]
\[f=\ln(u)~~~~~~~dg=du \\ \\ df=\frac{1}{u} du~~~~~~~g=u\]
-------------------------------------------------------------
\[u (\ln(u) )-\int\limits 1 \, du\]
\[uln(u)-u+c\]

Answer 6

ok, i got the same thing you did, which actually turns out to be (x+1)ln(x+1) - x - 1 instead of xln(x+1) -x+ln(x+1), so I guess they just got it wrong or something. Thanks!

Answer 7

Are (1,2) coordinates?

Answer 8

no, they're the limits of integration.

Answer 9

Okay
\[\Large (x+1)(\ln(x+1))-(x+1)|_1^2\]

Answer 10

ok, so I plugged that into my calculator, but the answers were still different: -.1925 as opposed to 0.9095

Answer 11

You should get 0.9095 did you typed it correctly?

Answer 12

I thought so, but maybe not. I used
fnInt((x+1)(ln(x+1)) - (x+1), x, 1, 2)?

Answer 13

(2+1)(ln(2+1))-(2+1)-[(1+1)(ln(1+1)-(1+1)]

Answer 14

oh never mind! haha i didn't use the integral

Answer 15

ok, I got it. Thanks!

Answer 16

welcome :)