1. ## integral

How to integrate sin(x)-log(x) within the limit 0 to 2? What is the value of the integral?

I am facing problem as log(x) is not defined at x=0.

2. ## Re: integral

I am facing problem as log(x) is not defined at x=0.
$\displaystyle \int_0^2\log x\;dx=\lim_{\epsilon \to 0^+}\int_{\epsilon}^2\log x\;dx$ .

3. ## Re: integral

Thanks for your hint. But does the integral possess any definite value?

4. ## Re: integral

Sure. Have you evaluated $\displaystyle \int_\epsilon ^ 2 \log x\ dx$ in terms of $\displaystyle \epsilon$?

Then just consider the limit of that as $\displaystyle \epsilon$ goes to zero.

5. ## Re: integral

Thanks.

Actually I need to evaluate [tex]\int_)^2 sin(x)-log(x)\dx[\tex] using Trapezoidal rule. I am facing problem as the integrand is not defined at [tex]x=0[\tex]. How to overcome this ?

Originally Posted by tom@ballooncalculus
Sure. Have you evaluated $\displaystyle \int_\epsilon ^ 2 \log x\ dx$ in terms of $\displaystyle \epsilon$?

Then just consider the limit of that as $\displaystyle \epsilon$ goes to zero.