21-122_02.12.19.pdf - Math 21-122 Handout 1 Improper Integrals There are two types of improper integrals Today we will review the first type which are

# 21-122_02.12.19.pdf - Math 21-122 Handout 1 Improper...

• 2

This preview shows page 1 - 2 out of 2 pages.

Math 21-122 Handout 02/12/19 1 Improper Integrals There are two types of improper integrals. Today we will review the first type, which are integrals with infinite intervals. Definition: If R t a f ( x ) d x exists for every number t a , then Z a f ( x ) d x = lim t →∞ Z t a f ( x ) d x, provided this limit exists as a finite number. If R b -∞ f ( x ) d x exists for every number t b , then Z b -∞ f ( x ) d x = lim t →-∞ Z b t f ( x ) d x, provided this limit exists as a finite number. These improper integrals are called convergent if the corresponding limit exists and divergent if the limit does not exist. 1.1 Practice Problems Determine whether or not the following integrals converge or diverge. If the integral converges, computeits value.1.Z-34x2+ 8x+ 17dx.2.Z12x3+x2dx.3.Z-∞xsinxdx. 1
2 The Comparison Test for Improper Integrals