# integral that converges……..

• January 15th 2007, 08:16 PM
m777
integral that converges……..
Hello,
Plz try to solve this question.
• January 15th 2007, 08:57 PM
CaptainBlack
Question#01:-

(a) Evaluate the integral that converges $\int_0^{\pi/2}\tan(x) dx$.

I don't understand the question, this integral diverges does it not?

RonL
• January 15th 2007, 09:07 PM
CaptainBlack
Question#01:-

(b) Find the value of "a", If $\int_0^{+\infty}\frac{1}{x^2+a^2} dx=1$.

Well this is a standard integral, and:

$\int_0^{\infty}\frac{1}{x^2+a^2} dx=\left[\frac{1}{a}\arctan(u/a)\right]_0^{+\infty}=\frac{\pi}{2}\frac{1}{a}$.

So the required value is $a=\pi/2$

RonL