Consider the improper integral J= _ 0 ^ x 1+x^ 2 ,dx.

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Consider the improper integral

J=\int_{0}^{\infty} \frac{x}{1+x^{2}}\,dx.

(a) Show that the integral is convergent or divergent. (b) If convergent, determine the exact value of

J