Integrate x^2sin(x) between -pi and pi

It is possible to solve this question using integration by parts. However, we note that sin(x) is an odd function, meaning that sin(-x) = -sin(x). Thus x2sin(x) is also an odd function. This means that the area under x2sin(x) from 0 to pi is equal to the area under x2sin(x) from -pi to 0. Hence the integral of x2sin(x) between -pi and pi is 0.

Related Further Mathematics A Level answers

All answers ▸

Show that the set of real diagonal (n by n) matrices (with non-zero diagonal elements) represent a group under matrix multiplication


find all the roots to the equation: z^3 = 1 + i in polar form


What are imaginary numbers, and why do we bother thinking about them if they don't exist?


A particle is moving in a straight line with simple harmonic motion. The period of the motion is (3pi/5)seconds and the amplitude is 0.4metres. Calculate the maximum speed of the particle.


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