How do I integrate by parts?

Lets use and example: y=xsin(x). If we try to integrate this normally, we find it very hard. The integration by parts method splits up the function we are integrating into manageable bits. The formula we use to work this out is:Integral(UdV)=UV-Integral(VdU)were the dU is the differential of U and dV is the differential of V. In our example y=xsin(x), we let U=x and dV=sin(x). To find dU we differentiate x (dU=1). To find V we integrate dV (V=-cos(x)). Now we just stick everything in the formula:Integral(xsin(x))= x(-cos(x))-Integral((-cos(x))1)=-xcos(x)+sin(x) +Cwhere C is an arbitrary constant. This is the answer.- See more at: https://www.mytutorweb.co.uk/tutors/secure/ta-yourexplanations.html#sthash.JreWATFA.dpuf

BW
Answered by Barnaby W. Maths tutor

4335 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Factorise 6x^2 + 7x - 3=0


Find the gradient of y=x^2-6x-16 at the point where the curve crosses the x-axis


Why do you differentiate in optimisation questions?


Why does ln(x) differentiate to 1/x ?


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