Integrate xsin(x).

The technique we need to use to solve this integral is called integration by parts. The parts formula is: the integral of (uv' dx) = uv - the integral of (u'v dx) (where u and v are functions of x). We need to decide which of our functions (x or sin(x)) is our u and which is our v'. To pick our 'u' we consider which function becomes simpler when we differentiate it. In this case this is x since its derivative is 1 whereas the derivative of sin(x) is cos(x) which isn't much simpler. So u = x, v' = sin(x). Which means u' = 1 , v = -cos(x). So our integral becomes: -xcos(x) - the integral of (-cos(x)dx). Giving our final answer of : -xcos(x) + sin(x) + c

JW
Answered by Jakub W. Further Mathematics tutor

2224 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the GS to the following 2nd ODE: d^2y/dx^2 + 3(dy/dx) + 2 = 0


The function f is defined for x > 0 by f (x) = x^1n x. Obtain an expression for f ′ (x).


Find a vector that is normal to lines L1 and L2 and passes through their common point of intersection where L1 is the line r = (3,1,1) + u(1,-2,-1) and L2 is the line r = (0,-2,3) + v(-5,1,4) where u and v are scalar values.


Integrate cos(4x)sin(x)


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