2010-10.md

course	course_year	question_number	tags	title	year
Complex Analysis or Complex Methods	IB	10	IB 2010 Complex Analysis or Complex Methods	Paper 1, Section II, A	2010

Calculate the following real integrals by using contour integration. Justify your steps carefully.

(a)

$$I_{1}=\int_{0}^{\infty} \frac{x \sin x}{x^{2}+a^{2}} d x, \quad a>0$$

(b)

$$I_{2}=\int_{0}^{\infty} \frac{x^{1 / 2} \log x}{1+x^{2}} d x$$