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.
HL
Answered by Harry L. • Further Mathematics tutor
7857 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸By use of matrices uniquely solve the following system of equations, justifying each step of the calculation: 3x-7y=6, 5y-2x=-3.
Given M = [[-2,6],[1,3]], find P and D such that M = PDP^(-1) where D is a diagonal matrix
How would you show the equation f(x) = 2x – 10 sin x – 2 has a root between 2 and 3 (where x is measured in radians)
A mass m=1kg, initially at rest and with x=10mm, is connected to a damper with stiffness k=24N/mm and damping constant c=0.2Ns/mm. Given that the differential equation of the system is given by d^2x/dt^2+(dx/dt *c/m)+kx/m=0, find the particular solution.