7. Integration

7.01 Introduction to anti-differentiation

7.02 Anti-differentiation and exponential functions

7.03 Anti-differentiation and trigonometric functions

7.04 Antidifferentiation and logarithmic functions

7.05 Further anti-differentiation

INVESTIGATION: Fundamental theorem of calculus

7.06 The fundamental theorem of calculus

7.07 Approximate areas under curves

7.08 The definite integral and areas under curves

7.09 Area between curves

7.10 Further definite integrals

7.11 Applications of integration

VCE 12 Methods 2023

7.01 Introduction to anti-differentiation

Interactive practice questions

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

Find the primitive function of $10x+7$10x+7.

Use $C$C as the constant of integration.

Easy

< 1min

Outcomes

U34.AoS3.6

anti-derivatives of polynomial functions and functions of the form f(ax+b) where f is x^n, e^x, sin(x), cos(x) and linear combinations of these

U34.AoS3.19

find anti-derivatives of polynomial functions and power functions, functions of the form f(ax+b) where f is x^n, e^x, sine or cosine, and simple linear combinations of these, using pattern recognition, or by hand

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