Mean Value of a Function (Edexcel A-Level Further Mathematics): Quizzes

📚Quizzes
Revision NotesModel AnswersQuizzesFlashcardsExam Questions
Mean Value of a Function
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

What does the mean value of f(x)f(x) over [a,b][a,b] represent?

Average value of f(x)f(x) in the interval

What is the formula for the mean value of f(x)f(x) over [a,b][a,b]?

1b−a∫abf(x) dx\frac{1}{b-a} \int_a^b f(x) \, dx

In the mean value formula, what does b−ab-a represent?

Length of the interval

The mean value represents a constant height for what shape?

Rectangle with same area over interval

What is the mean value of f(x)=x2f(x)=x^2 over [1,3][1,3]?

133\frac{13}{3}

What is the mean value of f(x)=sin⁡xf(x)=\sin x over [0,π][0,\pi]?

2π\frac{2}{\pi}

A common mistake is calculating only ∫abf(x)dx\int_a^b f(x) dx. What is missing?

Dividing by b−ab-a

Should you approximate π\pi in answers unless asked?

No, keep exact forms

What is the first step in evaluating mean value?

Set up the formula

What is the antiderivative of sin⁡x\sin x?

−cos⁡x+C-\cos x + C

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Volumes of Revolution

Methods in Calculus

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

Volumes of Revolution

Methods in Calculus

Explore Edexcel A-Level Further Mathematics Flashcards by Topics

Volumes of Revolution

Methods in Calculus

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Volumes of Revolution

Methods in Calculus

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.