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

Answered by Jonathan R. Maths tutor

4439 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the coordinates of the turning points of the curve y = 4/3 x^3 + 3x^2-4x+1


integration by parts: x^-2lnx


How to find and classify stationary points (maximum point, minimum point or turning points) of curve.


Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences