15D.1 - Approximating area
The area under a curve can be approximated using rectangles or trapeziums as shown below. The following three diagrams show approximations with an interval width of 1 unit.
As shown by the diagrams above, approximations can result in an overestimation or underestimation of the area. In general, the trapezium method will give the most accurate approximation.
15D.1 - Example 1: Approximation of the area under a curve
Consider the area under the curve \(y=x^2\) between \(x=0\) and \(x=3\).
■ Please note that the exact area can be calculated using integral calculus: \[A=\int_{0}^{3}x^2dx=9\] |
15D.1 - Example 1: Video solution
15D.1 - Example 1: Practice
Question 1: Find the 15D.1 - Example 1: Solutions
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