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4.065 Areas under curves

Interactive practice questions

Consider the function $y=f\left(x\right)$y=f(x) drawn below.

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a

Find the value of $\int_0^2f\left(x\right)dx$20f(x)dx.

b

Find the value of $\int_2^5f\left(x\right)dx$52f(x)dx.

c

Find the value of $\int_5^6f\left(x\right)dx$65f(x)dx.

d

Hence calculate the area bounded by the function and the $x$x-axis.

Easy
2min

Consider the function $y=f\left(x\right)$y=f(x) drawn below.

Easy
1min

Consider the function $y=f\left(x\right)$y=f(x) drawn below.

Easy
1min

Consider the function $y=f\left(x\right)$y=f(x) drawn below.

Easy
3min
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Outcomes

ACMMM125

interpret the definite integral ∫ {from a to b} f(x)dx as area under the curve y=f(x) if f(x)>0

ACMMM127

interpret ∫ {from a to b} f(x)dx as a sum of signed areas

ACMMM128

recognise and use the additivity and linearity of definite integrals

ACMMM131

understand the formula ∫ {from a to b} f(x)dx= F(b)−F(a) and use it to calculate definite integrals

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