Chapter 5: Q 18. (page 495)

Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is continuous on $[a, \infty)$ then,
$\int_{a}^{\infty} f (x) d x$

Short Answer

Expert verified

$\int_{a}^{\infty} f (x) d x = \lim_{k \to \infty} \int_{a}^{k} f (x) d x$

Step by step solution

Step 1. Given information.

Consider the given integral.

$\int_{a}^{\infty} f (x) d x$

Step 2. Defining improper integrals.

Since the given function is continuous on the given interval $[a, \infty)$ . Thus,

role="math" localid="1652091582807" $\int_{a}^{\infty} f (x) d x = \lim_{k \to \infty} \int_{a}^{k} f (x) d x$

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Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is continuous on $[a, \infty)$ then,
$\int_{a}^{\infty} f (x) d x$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Defining improper integrals.

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Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.If f is continuous ona,∞then,∫a∞fxdx

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Defining improper integrals.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Discrete Mathematics

Mechanics Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Defining improper integrals: Fill in the blanks, using limits and proper definite integrals to express each of the following types of improper integrals.
If f is continuous on $[a, \infty)$ then,
$\int_{a}^{\infty} f (x) d x$