Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.

  1. Factorising denominator of fraction:x^2 + 10x + 21 = (x+3)(x+7)2) Partial fractions:f(x) = 12/(x+3)(x+7);  let f(x) = A/(x+3) + B/(x+7)then equating the nominator: A(x+7) + B(x+3) = 12From this we can set up simultaneous equations: (1): Ax + Bx = 0; (2): 7A + 3B = 12From (1): A = -BSubstituting A into (2): 7(-B) + 3B =12So B=-3, and A=3f(x) = 3/(x+3) – 3/(x+7)3) Integrating the function:∫ f(x) dx = 3 ∫ (1/(x+3) - 1/(x+7)) dx = 3ln|x+3| - 3ln|x+7| + c4) Evaluating the integral with limits [-1,1]:3ln|1+3| - 3ln|1+7| - 3ln|-1+3| + 3ln|-1+7| = 3ln(3/2) = ln(27/8) = 1.22 (2d.p.)

Related Further Mathematics GCSE answers

All answers ▸

How to solve the inequality 1 - 2(x - 3) > 4x


Can you explain induction and go through an example?


A particle is moving in a straight line from A to B with constant acceleration 4m/s^2. The velocity of the particle at A is 3m/s in the direction AB. The velocity of the particle at B is 18m/s in the same direction/ Find the distance from A to B.


Find the tangent to the equation y=x^2 -2x +4 when 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