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

7.02 Anti-differentiation and exponential functions

Interactive practice questions

State the primitive function of $e^{2x}$e2x.

You may use $C$C as a constant.

Easy

< 1min

State the primitive function of $e^{-5x}$e−5x.

You may use $C$C as a constant.

Easy

< 1min

Determine $\int e^{-x}dx$∫e−xdx.

You may use $C$C as a constant.

Easy

< 1min

State the primitive function of $e^{0.25x}$e0.25x.

You may use $C$C as a constant.

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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