Book a Demo

Topics

4. Integration

4.01 Introduction to anti-differentiaion

Lesson

Worksheet

Practice

4.02 Antidifferentiation and exponential functions

4.03 Antidifferentiation and trigonometric functions

4.04 Further anti-differentiation

4.05 Area under a graph

4.06 The definite integral

4.065 Areas under curves

4.07 Further definite integrals

4.08 The fundamental theorem of calculus

INVESTIGATION: The fundamental theorem of calculus

Book a Demo

Australia QLD

Year 12

4.01 Introduction to anti-differentiaion

Lesson

Worksheet

Practice

Interactive practice questions

Find an equation for $f\left(x\right)$f(x) if $f'\left(x\right)=8x$f′(x)=8x.

Use $C$C as the constant of integration.

Easy

< 1min

Find the primitive function of $x^5$x5.

Use $C$C as the constant of integration.

Easy

1min

Find the primitive function of $9x^2$9x2.

Use $C$C as the constant of integration.

Easy

< 1min

If $f'\left(x\right)=9$f′(x)=9, find the primitive function $f\left(x\right)$f(x).

Use $C$C as the constant of integration.

Easy

< 1min

Outcomes

3.3.1.1

recognise anti-differentiation as the reverse of differentiation

3.3.1.2

use the notation ∫ 𝑓(𝑥) 𝑑x for anti-derivatives or indefinite integrals

3.3.1.3

establish and use the formula ∫ 𝑥^𝑛 𝑑x = 1/(n+1) 𝑥^(𝑛+1)+𝑐 for 𝑛≠−1

3.3.1.7

understand and use the formula for indefinite integrals of the form ∫ [ 𝑓(𝑥)+𝑔(𝑥) ] 𝑑x = ∫ 𝑓(𝑥) 𝑑x + ∫ 𝑔(𝑥) 𝑑x

3.3.1.9

determine 𝑓(𝑥), given 𝑓′(𝑥) and an initial condition 𝑓(𝑎) = b

4.01 Introduction to anti-differentiaion

Interactive practice questions

Outcomes

3.3.1.1

3.3.1.2

3.3.1.3

3.3.1.7

3.3.1.9

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