Evaluating Improper Integrals and Limits

The video tutorial explains how to determine if an improper integral converges or diverges. It focuses on an integral with an upper limit of positive infinity, replacing infinity with a variable, and evaluating the limit. The tutorial concludes that the integral diverges as the limit approaches infinity.

What makes an integral improper?

• The function is continuous.

• The upper limit is infinity.

• The integral is definite.

• The lower limit is zero.

What is the first step in evaluating an improper integral with an infinite upper limit?

• Replace infinity with a variable.

• Calculate the derivative.

• Find the definite integral.

• Use numerical methods.

What is the anti-derivative of 0.5e^x?

• 0.5x^2

• x^0.5

• e^x

• 0.5e^x

How do you evaluate the limit of an integral as the variable approaches infinity?

• By substituting the variable with zero.

• By calculating the derivative.

• By substituting the bounds and evaluating the expression.

• By using a calculator.

What happens to e^b as b approaches infinity?

• It approaches zero.

• It remains constant.

• It decreases without bound.

• It increases without bound.

Why does the improper integral in the video diverge?

• Because the function is bounded.

• Because the integral is definite.

• Because the limit approaches infinity.

• Because the limit exists.