Chapter 5: Q 19. (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 a continuous on $(- \infty, b]$ , then
$\int_{- \infty}^{b} f (x) d x =______$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Consider the given integral,

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

Step 2. Defining improper integrals.

Since the given function is continuous on the given interval $(- \infty, b]$ , then,

localid="1652093197157" $\int_{- \infty}^{b} f (x) d x = \lim_{k \to - \infty} \int_{k}^{b} f (x) d x$

Where kis any real number.

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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 a continuous on $(- \infty, b]$ , then
$\int_{- \infty}^{b} f (x) d x =______$

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 a continuous on -∞,b, then∫-∞bfxdx=______

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

Calculus

Decision Maths

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Logic and Functions

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 a continuous on $(- \infty, b]$ , then
$\int_{- \infty}^{b} f (x) d x =______$