Finding-Areas-Under-Graphs Wjec-Eduqas Higher

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Exam code:C300

Finding areas under graphs

How do I estimate the area under a graph?

To find an estimate for the area:
- Split area into vertical strips
- Draw straight lines between the tops of the strips
- Find area of strips (trapeziums) using Area = ½(a + b)h
- Add the areas

How do I know if my answer is an underestimate or an overestimate?

A common exam question is to ask if your estimate of the area is an underestimate or an overestimate
To answer this, simply look at the straight lines joining the tops of your strips
- If the straight lines are below the curve, it is an underestimate
- If the straight lines are above the curve, it is an overestimate
In your exam, the lines will all be below or all be above the curve- though it may be difficult to tell which for some strips

Examiner Tips and Tricks

This is particularly useful when working with speed-time and distance-time graphs if they are curves and not straight lines.

Worked Example

The graph below shows $y equals cube root of x$ for $0 less or equal than x less or equal than 1$

Graph showing a concave curve from the origin, increasing from y=0 at x=0 to y=1 at x=1, on a grid with labelled axes. This is the graph of the cube root of x.

Find an estimate for the area between the curve, the $x$ axis and the line $x equals 1$ . Use four strips of equal width.

Split the area into four strips using the width of 0.25 for each one

Find the $y$ coordinate at the end of each strip by reading the value from the graph or substituting the <img alt=”x” data-mathml=”<math ><semantics><mi>x</mi><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true,”toolbar”:”<toolbar ref=’general’><tab ref=’general’><removeItem ref=’setColor’/><removeItem ref=’bold’/><removeItem ref=’italic’/><removeItem ref=’autoItalic’/><removeItem ref=’setUnicode’/><removeItem ref=’mtext’ /><removeItem ref=’rtl’/><removeItem ref=’forceLigature’/><removeItem ref=’setFontFamily’ /><removeItem ref=’setFontSize’/></tab></toolbar>”}</annotation></semantics></math>” data-type=”commentary” height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2211%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3Ex%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%2F%3E%3C%2Fdefs%3E%3Ctext%20font-family%3D%22Times%20New%20Roman%22%20font-size%3D%2218%

Maths Gcse Wjec-Eduqas Higher

Finding-Areas-Under-Graphs Wjec-Eduqas Higher