# calculus

posted by .

how would you do this improper integral

1/(x-1)
from 0 to 2

this is improper at one, so I split it up into two integrals
ln(x-1) from 0-1 and
ln(x-1) from 1-2

I then did for the first one the (lim t->1(-) of ln(t-1))-(ln(0-1))

and then the same thing for the second part
I didn't know if this was right though, or what the answer would be

• calculus -

• calculus -

• calculus -

I left the final calculation up to you. If you define the integral as the sum of two parts that each approach within a distance a of x=1, and let a gapproach zero, than the answer will be zero because the two parts will always cancel, not matter how small a is.

## Similar Questions

1. ### Calculus

integral -oo, oo [(2x)/(x^2+1)^2] dx (a) state why the integral is improper or involves improper integral *infinite limit of integration (b) determine whether the integral converges or diverges converges?
2. ### calculus

how would you do this improper integral 1/(x-1) from 0 to 2 this is improper at one, so I split it up into two integrals ln(x-1) from 0-1 and ln(x-1) from 1-2 I then did for the first one the (lim t->1(-) of ln(t-1))-(ln(0-1)) and …
3. ### calc

how would you do this improper integral 1/(x-1) from 0 to 2 this is improper at one, so I split it up into two integrals ln(x-1) from 0-1 and ln(x-1) from 1-2 I then did for the first one the (lim t->1(-) of ln(t-1))-(ln(0-1)) and …
4. ### calculus

1. integral -oo, oo [(2x)/(x^2+1)^2] dx 2. integral 0, pi/2 cot(theta) d(theta) (a) state why the integral is improper or involves improper integral (b) determine whether the integral converges or diverges converges?
5. ### Calculus (improper integrals)

the integral from 0 to lnx of lnx/(x^1/2) thanks!
6. ### Calculus

I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5-(u^2))du I have a feeling I will be able to find …
7. ### Calculus

Integrals: When we solve for area under a curve, we must consider when the curve is under the axis. We would have to split the integral using the zeros that intersect with the axis. Would this be for all integrals?
8. ### improper integral

can any one explain how to evaluate this improper integral i.e. the function is not continuous at 0 neither at inf integration of [(e^(-sqrt(t)))/sqrt(t)]dt from 0 to infinity the integration part is easy but i want only how to evaluate …
9. ### Calculus 2

The question is: Evaluate the improper integral for a>0. The integral is: the integral from 0 to infinity, of e^(-y/a)dy Can anyone help me solve this?
10. ### Calculus

What is the connection between improper integrals, Riemann sums, and the integral test?

More Similar Questions