Topics
7. Integration
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AustraliaVIC
VCE 12 Methods 2023

7.08 The definite integral and areas under curves

Lesson
Worksheet
Practice

Interactive practice questions

Calculate $\int_0^3\left(4x+5\right)dx$∫30​(4x+5)dx.

Easy
1min

Calculate $\int_{-2}^0\left(10x+4\right)dx$∫0−2​(10x+4)dx.

Easy
1min

Calculate $\int_2^4\left(6x+5\right)dx$∫42​(6x+5)dx.

Easy
1min

Calculate $\int_3^4\left(-4x+3\right)dx$∫43​(−4x+3)dx.

Easy
1min
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Outcomes

U34.AoS3.7

informal consideration of the definite integral as a limiting value of a sum involving quantities such as area under a curve and approximation of definite integrals using the trapezium rule

U34.AoS3.9

properties of anti-derivatives and definite integrals

U34.AoS3.14

the concept of approximation to the area under a curve using the trapezium rule, the ideas underlying the fundamental theorem of calculus and the relationship between the definite integral and area

U34.AoS3.20

evaluate approximations to the area under a curve using the trapezium rule, find and verify antiderivatives of specified functions and evaluate definite integrals

U34.AoS3.21

apply definite integrals to the evaluation of the area under a curve and between curves over a specified interval

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