Question

Improper integral

Answer 1

\[\int\limits_{0}^{2} \frac{ 2x+1 }{ x^2+x-6 } dx\]

Answer 2

looks like a set up for a u - sub
try \(u=x^2+x-6\)

Answer 3

Yeah, I have that

Answer 4

\[\lim_{b \rightarrow \infty} [\ln|x^2+x-6|]\]

from 0 to b

Answer 5

where does the infinity come from?

Answer 6

That's a typo, oops. supposed to be a 2

Answer 7

\[\ln |b^2 + b -6| - \ln|6|\]

I have that, and the answer is -infinity, I'm confused on how that's the answer.

Answer 8

@satellite73 can you help?

Answer 9

HI!!

Answer 10

what are the limits of integration?

Answer 11

0 to b

Answer 12

to b??

Answer 13

oooh i see it is an improper integral since 2 is a zero of the denominator

Answer 14

yeah, its improper

Answer 15

rather \[\lim_{b \rightarrow 2} [\ln|b^2+b-6|]\]

Answer 16

on account of you cannot take the log of zero

Answer 17

Thanks

Answer 18

\[\color\magenta\heartsuit\]