### Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

### Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

### Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

# Weekly Challenge 29: Integral Equation

##### Stage: 5 Short Challenge Level:

Find the function $f(x)$ which solves the equation $$\int_0^x f(t)\,dt = 3f(x)+k\,,$$ where $k$ is a constant.

Did you know ... ?

In the same way that a differential equation is formed from differentials, an integral equation is formed from integrals. Problems in mathematics might naturally be specified in terms of integrals, others in terms of differentials. Differentials are mainly used when the problem involves only local changes, such as the force at a point, whereas integrals are used where the problem involves a global property of a system, such as the total energy.