Why is the definite integral between negative limits of a function with positive values negative even though the area bound by the x-axis is positive? for example the integral of y=x^2 between x=-2 and x=-1

Referring back to the definition of an integral, it is the sum of small elements on the x-axis (dx) multiplied by the value of the function at that point (y) commonly expressed as the sum of ydx. Since x is negative in this region, so is dx, resulting in all of the elements of the sum being negative. A useful way of remembering this is to think about the problem graphically, and what quadrant our function crosses:x,y > 0 Both ydx (and in turn the integral in this quadrant) is positivex > 0 > y Both ydx (and in turn the integral in this quadrant) is negativex < 0 < y Both ydx (and in turn the integral in this quadrant) is negativex,y < 0 Both ydx (and in turn the integral in this quadrant) is positive
(which is case 3 for the function y=x2 for negative limits)

Related Maths A Level answers

All answers ▸

Solve the following equation: x^3 + 8x^2 + 4x - 48=0


How would I differentiate something with the product rule?


A block of mass 5kg is at rest on a smooth horizontal table, and connected to blocks of 3kg and 4kg which are hanging by strings via pulleys on either end of the table. Find the acceleration of the system and the tension in each string.


evaluate the integral of lnx


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