MYTUTOR SUBJECT ANSWERS

208 views

Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one to (5-2x)^-1 you would get zero. Therefore, when you are integrating a fraction with a linear expression as the denominator (meaning a denominator where the greatest power of x is 1), it integrates to the natural logarithm (ln) of the denominator, multiplied by the differential of the denominator.

So in this example, 1/(5-2x) would integrate to

[ln(5-2x)/(-2)] (as 5-2x differentiates to -2) for 3≤x≤4

Then you would sub in the limits of x and subtract as usual:

ln(5-2(4))/(-2) - ln(5-2(3))/(-2)

= -1/2ln(5-8) - -1/2ln(5-6) 

Remeber that you cannot take the ln of a negative number, so it is best to write it as: 

= -1/2ln|-3| - -1/2ln|-1|

= -1/2ln(3) - -1/2ln(1)

ln(1)=0 so our answer is

-1/2ln3

  

Emily-Louisa S. A Level Maths tutor, A Level Further Mathematics  tutor

5 months ago

Answered by Emily-Louisa, an A Level Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

294 SUBJECT SPECIALISTS

£20 /hr

Celine A.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“Hello! I'm Celine and I am currently in my second year of my Maths degree at the University of Bristol.  I offer any level of Maths tutoring up to and including Maths and Further Maths A-level.  We can go through your course and home...”

MyTutor guarantee

£20 /hr

Munroop P.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Spanish+ 1 more

Maths
Spanish
Economics

“I am an Economics student at Warwick University. I am passionate about Economics but I also love Maths and Spanish, and so I am thrilled to be able to take Maths and Spanish modules within my Economics degree course.  I have experienc...”

£20 /hr

Youssef M.

Degree: Dentisty (Bachelors) - Birmingham University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“Who am I?Hello everyone, I'm Youssef and I'm a dental student at the University of Birmingham. Since a young age I've had a passion for science, one which I hope I can pass on to you too. A passion which I continue through studying d...”

MyTutor guarantee

About the author

Emily-Louisa S.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Exeter University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am in my first year of my mathematics degree at the University of Exeter and one of my favourite things about maths is how it can appear in unexpected situations. For example, in cryptography (the writing and solving of codes of whi...”

You may also like...

Posts by Emily-Louisa

Given that f(x)=2sinhx+3coshx, solve the equation f(x)=5 giving your answers exactly.

Integrate 1/(5-2x) for 3≤x≤4

Other A Level Maths questions

How would you differentiate ln(x^2+3x+5)?

How many lines of method should I write in order to get all of the marks?

Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok