How can I find the area under the graph of y = f(x) between x = a and x = b?

You can find the area under this graph by evaluating the definite integral of y = f(x) with respect to x between x = a and x = b

Please note: An area below the x-axis has a negative value

Example:

Find the area under the graph of y = x^2 between x = 3 and x = 6

 

Step 1: Integrate x^2 to give 1/3x^3

Step 2: Find the definite integral by substituting in values of x 

Area = 1/3.6^3 - 1/3.3^3 = 72 - 9 = 63