Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side.

 A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1)

Therefore the numerator = (A+2B)x+(3A+B)

Equating this numorator with the Left hand side we are presented with the two simultaneous equations A+2B=2, 3A+B=11 yielding solutions of B=-1, A=4 by elimination of A

 Hence the integral from 0 to 2  (2x + 11)/ (2x + 1)(x + 3) dx =  integral from 0 to 2 of 4/(2x+1) - 1/(x+3) dx

=[2ln(2x+1) - ln(x+3)] from 0 to 2

= [(2ln5-ln5)-(2ln1-ln3)]

=ln(5)-ln(1/3)

=ln(15)

GD
Answered by George D. Maths tutor

6309 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

It is given that n satisfies the equation 2*log(n) - log(5*n - 24) = log(4). Show that n^2 - 20*n + 96 = 0.


Solve the complex equation z^3 + 32 + 32i(sqrt(3)) = 0


Find the equation of the straight line perpendicular to 3x+5y+6=0 that passes through (3,4)


Find dy/dx in terms of t for the curve given by the parametric equations x = tan(t) , y = sec(t) for -pi/2<t<pi/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