Chapter 4: Q. 52 (page 315)

Indefinite integrals of combinations: Fill in the blanks to complete the integration rules that follow. You may assume that f and g are continuous functions and that k is any real number.
$\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = . . .$

Short Answer

Expert verified

The complete integration rule is $\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = f (x) g (x) + C$ .

Step by step solution

Step 1. Given information.

Consider the given indefinite integral is $\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = . . .$ .

Step 2. Fill the blank for the indefinite integral ∫f'xgx+fxg'xdx.

The theorem of Reversing the Product rule for Indefinite Integrals states that, $\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = f (x) g (x) + C$ .

Therefore, it can be said the appropriate fill in black will be $\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = f (x) g (x) + C$ .

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Indefinite integrals of combinations: Fill in the blanks to complete the integration rules that follow. You may assume that f and g are continuous functions and that k is any real number.
$\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = . . .$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill the blank for the indefinite integral ∫f'xgx+fxg'xdx.

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Indefinite integrals of combinations: Fill in the blanks to complete the integration rules that follow. You may assume that f and g are continuous functions and that k is any real number.∫f'xgx+fxg'xdx=...

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Fill the blank for the indefinite integral ∫f'xgx+fxg'xdx.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Probability and Statistics

Applied Mathematics

Decision Maths

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

Indefinite integrals of combinations: Fill in the blanks to complete the integration rules that follow. You may assume that f and g are continuous functions and that k is any real number.
$\int (f^{'} (x) g (x) + f (x) g^{'} (x)) d x = . . .$