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- 5.11 Definite Integrals.

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Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Trapezium Rule Practise using the trapezium rule to find an approximate value for the area under a curve.
- Integration Exercises on indefinite and definite integration of basic algebraic and trigonometric functions.
- Integration Video You can't possibly learn all about integration from a 28 minute video so all that this resource can do is provide a quick revision to help you do the online exercise.

Here are some exam-style questions on this topic:

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*The graph of \(f(x)=8-x^2\) crosses the x-axis at the points A and B.*" ... more - "
*The acceleration, \(a\) ms*" ... more^{-2}, of an object at time \(t\) seconds is given by - "
*Find:*" ... more - "
*The diagram below shows part of the graph of \(y = \dfrac{2x}{9-x^2}\)*" ... more - "
*The function \(f\) is defined by \(f(x) = 8 - 5 \sin{x} \), for \( x \ge 0 \).*" ... more - "
*A particle moves in a straight line such that its velocity, \(v\) ms*" ... more^{-1}, at time \(t\) seconds is given by: - "
*(a) Use the trapezium rule with 4 ordinates to estimate to 2 decimal places the value of*" ... more - "
*Consider the graph of the function \(f(x)=x^2+2\).*" ... more - "
*(a) Express the algebraic fraction*" ... more - "
*Make a sketch of a graph showing the velocity (in \(ms^{-1}\)) against time of a particle travelling for six seconds according to the equation:*" ... more - "
*Find the value of \(a\) if \(\pi \lt a \lt 2\pi\) and:*" ... more - "
*This graph represents the function \(f:x\to a \cos x, a\in \mathbf N\)*" ... more - "
*Consider the function \(f\) defined by \(f(x) = 25e^{x-5}\) for \(x \in \mathbb{R}^+\).*" ... more - "
*The following diagram shows the graph of \(f(x) = \cos(e^x) \; \text{for} \; 0 \le x \le 0.5\).*" ... more - "
*Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).*" ... more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.