Use integration to find I = ∫ xsin3x dx

Use integration by parts, let U = x, the derivative of U = 1, let the derivative of V = sin3x and intergrate the derivative of V to arrive at V = (-1/3)(cos3x). Substitute the value into the formula uv − ∫ vdu dx dx, arrive at I = (x)(-1/3)(cos3x) - ∫(1)(-1/3)(cos3x)dx which can be written us I = (-x/3)(cos3x) +∫(1/3)(cos3x)dx. ∫(1)(1/3)(cos3x)dx = (1/9)(sin3x). Now put that into the original equation giving the final answer I = (-x/3)(cos3x)+ (1/9)(sin3x) + c,

Answered by Zifeng L. Maths tutor

5904 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).


Differentiate 5x^3 + 4x^2 + 5x + 9


A curve has the equation y=7-2x^5, find dy/dx of this curve


What is the gradient of y = xcos(x) at x=0?


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