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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_0^5f\left(x\right)dx$50f(x)dx.

b

Find the value of $\int_5^7f\left(x\right)dx$75f(x)dx.

c

Hence calculate $\int_0^7f\left(x\right)dx$70f(x)dx.

d

Calculate the area bounded by the function and the $x$x-axis.

Easy
1min

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

Easy
3min

Answer the following questions:

Easy
1min

Answer the following questions:

Easy
2min
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Outcomes

3.3.2.3

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

3.3.2.5

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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