4.05 Area under a graph

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

Easy

< 1min

examine the area problem, and use sums of the form ∑_i 𝑓(𝑥_𝑖) 𝛿𝑥_𝑖, to estimate the area under the curve 𝑦=𝑓(𝑥)

use the trapezoidal rule for the approximation of the value of a definite integral numerically

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

recognise the definite integral ∫ (from a to b) 𝑓(𝑥) 𝑑x as a limit of sums of the form ∑_i 𝑓(𝑥_𝑖) 𝛿𝑥_i