Find a tutor
How it works
Prices
Resources
For schools
Become a tutor
Answers
>
Further Mathematics
>
GCSE
>
Article
Find the definite integral of f(x) = 12/(x^2+10x+21) with limits [-1,1]. Give your answer to 2 decimal places.
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) = 12
From this we can set up simultaneous equations: (1):
Ax + Bx = 0
; (2):
7A + 3B = 12
From (1):
A = -B
Substituting A into (2):
7(-B) + 3B =12
So
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| + c
4)
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.)
CG
Answered by
Camilla Giulia B.
•
Further Mathematics tutor
2030 Views
See similar Further Mathematics GCSE tutors
Related Further Mathematics GCSE answers
All answers ▸
The equation of a curve is y = x^2 - 5x. Work out dy/dx
Lengths of two sides of the triangle and the angle between them are known. Find the length of the third side and the area of the triangle.
Given that xy=2 and y=3x+5, find x and y. Do not use trial and improvement.
Point A lies on the curve: y=x^2+5*x+8. The x-coordinate of A is -4. What is the equation of the normal to the curve at A?
We're here to help
Contact us
Message us on Whatsapp
+44 (0) 203 773 6020
Company Information
Careers
Blog
Subject answers
Become a tutor
Schools
Safeguarding policy
FAQs
Using the Online Lesson Space
Testimonials & press
Sitemap
Popular Requests
Maths tutor
Chemistry tutor
Physics tutor
Biology tutor
English tutor
GCSE tutors
A level tutors
IB tutors
Physics & Maths tutors
Chemistry & Maths tutors
GCSE Maths tutors
© MyTutorWeb Ltd 2013–2025
Terms & Conditions
|
Privacy Policy
CLICK CEOP
Internet Safety
Payment Security
Cyber
Essentials
Cookie Preferences