The First Type of Improper Integral (12.3.1)

Question 1

• An improper integral is a definite integral with one of the following properties: the integration takes place over an infinite interval, or the integrand is undefined at a point within the interval of integration.

Answer 1

• An improper integral is a definite integral with one of the following properties: the integration takes place over an infinite interval, or the integrand is undefined at a point within the interval of integration.

Question 2

• With some improper integrals, the area of the region under the curve is finite even though the region extends to infinity.

Answer 2

• With some improper integrals, the area of the region under the curve is finite even though the region extends to infinity.

Question 3

• An improper integral that is infinite diverges. An improper integral that equals a numerical value converges.

Answer 3

• An improper integral that is infinite diverges. An improper integral that equals a numerical value converges.