- #1
wubie
Hello,
It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate.
double integral 1/(x+y) dA
where
R = [1,2] X [0,1]
So what I did first was integrate with respect to y first. I ended up with
ln(x+y)
with an upper limit of 1 and a lower limit of 0. Once simplified I get
ln(x+1) - ln x or ln( (x+1)/x )
Now I have to integrate with respect to x. But I can't remember how to take the integral of a natural log function. How do I proceed from here?
I can't remember if I can do the following:
Let G(x) = integral of ln( (x+1)/x ) dx
then
e^G(x) = integral of e^ln( (x+1)/x ) dx
which would simplify to
integral of (x+1)/x dx.
After I get a solution to the above equation I would then take the log of
ln e^G(x) = ln (answer)
to get
G(x) = ln (answer).
Can I do that? I can't remember. If not, how do I proceed from here?
Any help is appreciated. Thankyou.
It has been over a year since I last took calculus. And I don't recall how to take the integral of a natural logarithmic function. Here is the question that I am supposed to integrate.
double integral 1/(x+y) dA
where
R = [1,2] X [0,1]
So what I did first was integrate with respect to y first. I ended up with
ln(x+y)
with an upper limit of 1 and a lower limit of 0. Once simplified I get
ln(x+1) - ln x or ln( (x+1)/x )
Now I have to integrate with respect to x. But I can't remember how to take the integral of a natural log function. How do I proceed from here?
I can't remember if I can do the following:
Let G(x) = integral of ln( (x+1)/x ) dx
then
e^G(x) = integral of e^ln( (x+1)/x ) dx
which would simplify to
integral of (x+1)/x dx.
After I get a solution to the above equation I would then take the log of
ln e^G(x) = ln (answer)
to get
G(x) = ln (answer).
Can I do that? I can't remember. If not, how do I proceed from here?
Any help is appreciated. Thankyou.