Let's learn how to calculate the Area between a Curve and a Straight Line in A-Level Maths!
Area between a Curve and a Straight Line
To work out the Region between 2 lines, you work out the region below the ‘higher’line, and subtract the region below the ‘lower’ line
💡Sometimes you will need to work out the values of a and b
💡Sometimes a and b will be different for each part
💡MAKE SURE you put y1 and y2 the correct way around!
Example Question
Below is a diagram showing the equation y = x, as well as the curve y = x(4 – x). Find the Area bounded by the two lines.
1) Find where the lines cross (set the equations equal)
2) Integrate to find the Area
Example Question
The diagram shows a sketch of thecurve with equation y = x(x – 3), and the line with Equation 2x. Calculate the Area of region R.
1) Work out the coordinates of the major points..
As the curve is y = x(x – 3), the x-coordinate at C = 3
Set the equations equal to find the x-coordinates where they cross…
2) Area of the Triangle…
3) Area under the curve
Therefore area of R is 25 - 26/3 = 16 1/3
Drafted by Eunice (Maths)