Integrate the following expression with respect to x by parts: (2*x)*sin(x)

The integration by parts formula: S:udv/dx = uv -  S:v*du/dx, where S: means "Integral of with respect to x" 

Let 2*x be u and sin(x) be dv/dx

So du/dx =2 and v= -cos(x)

So S:(2x)sin(x) = (2x)(-cos(x)) - S:-cos(x)*2

= -2xcos(x) + 2*sin(x)

= 2sin(x) - 2x*cos(x) +c

DP
Answered by David P. Maths tutor

2985 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the stationary points of the curve y (x)= 1/3x^3 - 5/2x^2 + 4x and classify them.


Mechanics 1: How do you calculate the magnitude of impulse exerted on a particle during a collision of two particles, given their masses and velocities.


Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.


How would the integral ∫x^2sin2xdx be solved using integration by parts?


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