Shaun F. GCSE Maths tutor, A Level Maths tutor

Shaun F.

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Mathematics with International Study (Masters) - Exeter University

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About me

Hi, I'm Shaun! I'm currently in my third year of studying for a masters in Mathematics at the University of Exeter.

Hi, I'm Shaun! I'm currently in my third year of studying for a masters in Mathematics at the University of Exeter.

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About my sessions

I believe that it is very important in mathematics to understand what you are taught, not just blindly learn formulae! As such, I focus on teaching the ideas behind the method, not just the method itself.  I also think it's very important to practise questions yourself, so the sessions are interactive.  The actual structure of the sessions is up to you! I can go through exam papers or focus on particular topics you struggle with. If you have any questions, feel free to contact me. You can also arrange a free 'Meet the Tutor' session through this website to get to know me a little before you decide whether to go ahead with some sessions.

I believe that it is very important in mathematics to understand what you are taught, not just blindly learn formulae! As such, I focus on teaching the ideas behind the method, not just the method itself.  I also think it's very important to practise questions yourself, so the sessions are interactive.  The actual structure of the sessions is up to you! I can go through exam papers or focus on particular topics you struggle with. If you have any questions, feel free to contact me. You can also arrange a free 'Meet the Tutor' session through this website to get to know me a little before you decide whether to go ahead with some sessions.

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Personally interviewed by MyTutor

We only take tutor applications from candidates who are studying at the UK’s leading universities. Candidates who fulfil our grade criteria then pass to the interview stage, where a member of the MyTutor team will personally assess them for subject knowledge, communication skills and general tutoring approach. About 1 in 7 becomes a tutor on our site.

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Qualifications

SubjectQualificationGrade
MathematicsA-level (A2)A*
Further MathematicsA-level (A2)A
PhysicsA-level (A2)B
ITA-level (A2)B

General Availability

Pre 12pm12-5pmAfter 5pm
mondays
tuesdays
wednesdays
thursdays
fridays
saturdays
sundays

Subjects offered

SubjectQualificationPrices
Further MathematicsA Level£20 /hr
MathsA Level£20 /hr
MathsGCSE£18 /hr

Questions Shaun has answered

What is the integral of x sin(x) dx?

Find the following integral: ∫ x sin(x) dx

This question is a good candidate for the integration by parts method, as it is the product of two different 'parts'.

Recall that if you have an integral of the form

∫ u(dv/dx) dx

it can be written as

uv – ∫ v(du/dx) dx.

We need to decide which part we will differentiate (as in, which part is u), and which part we will integrate (as in, which part is dv/dx). 

We can note that continuously differentiating sin(x) results in a loop of cos(x), –sin(x), –cos(x), sin(x)..., whereas differentiating x once gives 1.

From this, it seems to make sense that we would want to differentiate the x part (so u is x) and therefore integrate the sin(x) part (so dv/dx is sin(x) ). So, let

u = x, which implies du/dx = 1

and let

dv/dx = sin(x). Integrating this to get v gives v = –cos(x).

So our integral is now of the form required for integration by parts.

∫ x sin(x) dx 

=  ∫ u(dv/dx) dx

= uv –  ∫ v(du/dx) dx

= –x cos(x) –  ∫ –cos(x)*1 dx

= –x cos(x) –  ∫ –cos(x) dx

= –x cos(x) +  ∫ cos(x) dx

The integral of cos(x) is equal to sin(x). We can check this by differentiating sin(x), which does indeed give cos(x). Finally, as with all integration without limits, there must be a constant added, which I'll call c. So the final answer is 

∫ x sin(x) dx = –x cos(x) +  sin(x) + c

Find the following integral: ∫ x sin(x) dx

This question is a good candidate for the integration by parts method, as it is the product of two different 'parts'.

Recall that if you have an integral of the form

∫ u(dv/dx) dx

it can be written as

uv – ∫ v(du/dx) dx.

We need to decide which part we will differentiate (as in, which part is u), and which part we will integrate (as in, which part is dv/dx). 

We can note that continuously differentiating sin(x) results in a loop of cos(x), –sin(x), –cos(x), sin(x)..., whereas differentiating x once gives 1.

From this, it seems to make sense that we would want to differentiate the x part (so u is x) and therefore integrate the sin(x) part (so dv/dx is sin(x) ). So, let

u = x, which implies du/dx = 1

and let

dv/dx = sin(x). Integrating this to get v gives v = –cos(x).

So our integral is now of the form required for integration by parts.

∫ x sin(x) dx 

=  ∫ u(dv/dx) dx

= uv –  ∫ v(du/dx) dx

= –x cos(x) –  ∫ –cos(x)*1 dx

= –x cos(x) –  ∫ –cos(x) dx

= –x cos(x) +  ∫ cos(x) dx

The integral of cos(x) is equal to sin(x). We can check this by differentiating sin(x), which does indeed give cos(x). Finally, as with all integration without limits, there must be a constant added, which I'll call c. So the final answer is 

∫ x sin(x) dx = –x cos(x) +  sin(x) + c

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2 years ago

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