Area L

Draw the graph of a continuous increasing function in the first quadrant and horizontal and vertical lines through two points. The areas in your sketch lead to a useful formula for finding integrals.

Integral Sandwich

Generalise this inequality involving integrals.

Integral Inequality

An inequality involving integrals of squares of functions.

Integral Equation

Stage: 5 Challenge Level:

Solve the following integral equation for $f(x)$: $$\int_0^x f(t)\,dt = 3f(x)+k\,,$$ where $k$ is a constant.