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
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/649215_230951.jpeg)
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/391071_874204.jpeg)
💡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.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/73710_35051.png)
1) Find where the lines cross (set the equations equal)
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/783854_337608.jpeg)
2) Integrate to find the Area
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/814076_43465.jpeg)
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.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/216111_515055.jpeg)
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…
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/184130_508876.jpeg)
2) Area of the Triangle…
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/673789_233310.jpeg)
3) Area under the curve
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/248862_134708.jpeg)
Therefore area of R is 25 - 26/3 = 16 1/3
Drafted by Eunice (Maths)