Integrate xsin(2x) by dx between the limits 0 and pi/2.

First it is important to identify that this is an integration by parts question as it can't be solved by substitution.
Let I = integral for ease of notation.Write out integration by parts formula I(u)dv= uv -I(v)du. You therefore need to select v and u so that you can integrate by du later on in your analysis.
In this case if we select u = x; du = dx. And if we select dv = sin2x; v = -cos(2x)/2.Then write in form as above I(u)dv = -(xcos(2x))/2 + I(cos(2x) /2 ) dx = -(xcos(2x))/2 +sin(2x)/4
Then sub in the limits to this expression to arrive at an answer of pi/4.

Answered by Benedict A. Maths tutor

6541 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the equation of the tangent to the circle x^2 + y^2 + 10x + 2y + 13 = 0 at the point (-3, 2)


y = 2x^3 + 15x^2 + 24x + 10 Find the stationary points on this curve and determine their nature


integrate xsin(x)


Find dy/dx when y = 5x^6 + 4x*sin(x^2)


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