Get This Right If You Want To Study At Cambridge University
A Calculus Challenge For High Schoolers
Today’s Challenge
This is a somewhat challenging calculus question that tests our understanding of integrals and function from the Test of Mathematics for University Admission (TMUA), which serves as part of the selection process for students wanting to study computer science at the University of Cambridge.
Give this problem a try before jumping in for the solution!
Solution
Let’s start with the given condition that xf(x) > 0 for all non-zero values of x.
This gives us information on the general shape of the function, which is
We are only concerned with the interval [-2, 2].
The first integral tells us that the difference of B and A is 4
The second integral takes the absolute value of f(x), which means the area A is now above the x-axis.
The question wants us to find the integral of f(|x|) from -2 to 0. Let’s think about the graph transformation. In fact, taking the modulus sign within the function means that we remove the left half of the graph and replace it with the right half.
This means the question wants us to find the value of B!
Well done!
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Happy reading,
Barry 🍩