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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 WA

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 $f'\left(x\right)=4x$f′(x)=4x.

Use $c$c as the constant of integration.

Easy

1min

Find the primitive function of $x^7$x7.

Use $c$c as the constant of integration.

Easy

1min

Find the primitive function of $25x^4$25x4.

Use $c$c as the constant of integration.

Easy

1min

If $f'\left(x\right)=4$f′(x)=4, find the primitive function $f\left(x\right)$f(x).

Use $c$c as the constant of integration.

Easy

< 1min

Outcomes

3.2.1

identify anti-differentiation as the reverse of differentiation

3.2.2

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

3.2.3

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

3.2.6

identify and use linearity of anti-differentiation

3.2.8

identify families of curves with the same derivative function

3.2.9

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

4.01 Introduction to anti-differentiaion

Interactive practice questions

Outcomes

3.2.1

3.2.2

3.2.3

3.2.6

3.2.8

3.2.9

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