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)