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

JR
Answered by Jonathan R. Maths tutor

4630 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

using integration by parts evaluate the integral of xsinx between x=0 and x =pi/2


How do I maximise/minimise a given function f(x)?


A curve C has equation y = (2 - x)(1 + x) + 3 . A line passes through the point (2, 3) and the point on C with x-coordinate 2 + h . Find the gradient of the line, giving your answer in its simplest form.


The equation of a curve C is (x+3)(y-4)=x^2+y^2. Find dy/dx in terms of x and y


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences