Lecture 25.3 - Inequalities with Integrals

We show that if f is less than or equal to g on [a, b] then the integral of f on [a, b] is less than or equal to the integral of g on [a, b]. We also show that if a nonnegative continuous function has zero integral on [a, b] then the function must in fact be identically zero. Lastly, we prove the triangle inequality for integrals.