Integration can be used to find areas, volumes, central points and many useful things. Let's learn about definite integrals in A-Level Maths.
Definite Integral
A Definite Integral has start and end values: in other words there is an interval [a, b].
a and b (called limits, bounds or boundaries) are put at the bottom and top of the "S", like this:
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/99300_264899.png)
There are 3 stages to find the Definite Integral by calculating the Indefinite Integral at a, and at b…
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/161223_103648.jpeg)
1. The statement. Basically the function written out, with values for a and b
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/257456_525759.jpeg)
2. After integration. The function is integrated and put into square brackets
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/728142_102141.jpeg)
3. The evaluation. Round brackets are used to split the integration in two. One part for b and one for a.
Example Question
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/707971_174659.jpeg)
Evaluate the above ⬆️
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/390054_163345.jpeg)
Integrate the function and put it in square brackets. Put the ‘limits’ outside thebracket.
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/432889_733419.jpeg)
Example Question
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/885115_475265.jpeg)
The Indefinite Integral is: ∫cos(x) dx = sin(x) + C
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/596423_702236.png)
Example Question
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/865468_535613.jpeg)
![broken image](http://custom-images.strikinglycdn.com/res/hrscywv4p/image/upload/c_limit,fl_lossy,h_9000,w_1200,f_auto,q_auto/4979856/862690_963043.jpeg)
Drafted by Eunice (Maths)
Reference
https://www.mathsisfun.com/calculus/integration-definite.html