Q. 51 - Calculus

Question

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.

$\int \left(f\left(x\right)+g\left(x\right)\right)dx=...$ 

Step-by-Step Solution

Answer

The complete integration rule is $\int \left(f\left(x\right)+g\left(x\right)\right)dx=\int f\left(x\right)dx+\int g\left(x\right)dx$.

Step 1. Given information.

Consider the given indefinite integral is $\int \left(f\left(x\right)+g\left(x\right)\right)dx$.

Step 2. Fill the blank for the indefinite integral ∫ f ( x ) + g ( x ) d x .

The theorem of sum rule for Indefinite Integrals states that, $\int \left(f\left(x\right)+g\left(x\right)\right)dx=\int f\left(x\right)dx+\int g\left(x\right)dx$.

Therefore, it can be said the appropriate fill in black will be $\int \left(f\left(x\right)+g\left(x\right)\right)dx=\int f\left(x\right)dx+\int g\left(x\right)dx$.