Topics
4. Integration
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AustraliaAU
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
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Outcomes

ACMMM114

recognise anti-differentiation as the reverse of differentiation

ACMMM115

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

ACMMM116

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

ACMMM119

recognise and use linearity of anti-differentiation

ACMMM121

identify families of curves with the same derivative function

ACMMM122

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

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