Topics
7. Integration
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AustraliaVIC
VCE 12 Methods 2023

7.07 Approximate areas under curves

Lesson
Worksheet
Practice

Interactive practice questions

Consider the function drawn below:

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Calculate geometrically, the area bounded by the curve and the $x$x-axis over $0\le x\le4$0≤x≤4.

Easy
1min

Consider the function drawn below:

Easy
1min

Find the exact value of $\int_0^6\left(6-x\right)dx$∫60​(6−x)dx geometrically.

Easy
1min

Find the exact value of $\int_0^{12}f\left(x\right)dx$∫120​f(x)dx geometrically, where $y=f\left(x\right)$y=f(x) is graphed below.

Easy
< 1min
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Outcomes

U34.AoS3.10

application of integration to problems involving finding a function from a known rate of change given a boundary condition, calculation of the area of a region under a curve and simple cases of areas between curves, average value of a function and other situations.

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

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