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# Indefinite Integrals

## 10.1 Algebraic Properties of Antiderivatives

#### Algebraic Properties of Indefinite Integrals

• There are a few algebraic properties for antiderivatives:

i) Sum

\int f(x)+g(x) d x=\int f(x) d x+\int g(x) d x

ii) Difference

\int f(x)-g(x) d x=\int f(x) d x-\int g(x) d x

iii) Scalar Multiple

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## 8.1 Anti-Differentiation Concepts

#### Anti-Differentiation

• The area under a graph within an interval x \in [a,b] can be estimated by a sum of rectangles for smaller intervals of v.
• Differentiation is the process of finding the derivative function from the original function. Conversely, the process of finding a function from its derivative is called anti-differentiation.
• f(x) is known as the antiderivative of f^{\prime}(x).
• A derivative function might have several antiderivatives (see example).

## 6.1 Antiderivatives of Functions

#### Antiderivatives of Specific Functions

• We will be looking at antiderivatives of polynomial, exponential and trigonometric functions.
• The formulas are as below:
##### i) Polynomial functions

\int x^{n} d x=\frac{1}{n+1} x^{n+1}+c \quad,\ n \neq-1

\int x^{-1} d x=\int \frac{1}{x} d x=\ln |x|+c

Note: Notice that in there is an absolute value over to make the result fit the domain for all logarithmic functions is (0,\ +\infty), and x=0 is not possible in the first place as it would make \frac{1}{x} undefined.

##### ii) Exponential functions
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## Integration [Video Tutorial]

This tutorial covers material encountered in chapter 11 of the VCE Mathematical Methods Textbook, namely: Integration If you’re thinking “that’s all?” do not be deceived.… Read More »Integration [Video Tutorial]