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Area bounded by a Curve

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A Level Maths



Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths students

A-Level Maths Edexcel C2 January 2008 Q7c
This question is on the area between a curve and a line using integration.
In figure 2, the curve C has equation y = 6x - x2 and the line L has equation y = 2x. The region r, bounded by the curve C and the line L, is shown shaded in figure 2.
Use calculus to find the area of R.
A-Level Maths Edexcel C2 June 2008 Q8b
This question is on areas under a graph using integration methods.
Figure 2 shows a sketch pf part of the curve with equation y = 10 + 8x + x2 - x3.
The curve has a minimum turning point A.
The region R, shown shaded in Figure 2, is bounded by the curve, the y-axis and the line from O to A where O is the origin
Using calculus, find the exact area of R.



C2 Integration - Areas above + below curves
This video shows how to find areas above and below curve, this is typical of an exam situation.
C2 Integration - area between and curve and a line
Example:
1. The diagram shows a sketch of part of the curve with equation y = x(4 - x) and the line with equation y = x.
Find the area of the region bounded by the curve and the line.
2. The diagram shows a sketch of part of the curve with equation y = x(x - 3) and the line with equation y = 2x.
Find the area of the shaded region OAC.


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