Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (xln(x) - int(x(1/x))) = x*ln(x) - x

Therefore, evaluating between 2 and 4 gives us (4ln(4) - 4) - (2ln(2) - 2) = 2ln(16/2) - 4 + 2 = ln(64) - 2. So a = 64 and b = 2

KR
Answered by Kyle R. Maths tutor

3696 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How would I differentiate a function such as f(x)=x^3(e^(2x))?


The rate of decay of the mass is modelled by the differential equation dx/dt = -(5/2)x. Given that x = 60 when t = 0, solve the quation for x in terms of t.


How do I identify that the coordinate (2,3) is the maximum point of the curve f(x)?


How do I check if events are independent (in statistics / probability)?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning