# FA6

From Example Problems

Use the inequality for to prove that

for and , and then use this to prove the triangular inequality:

## First Part

Let and be such that .

Let and .

Using the inequality, .

Now integrate from to .

Set and .

Plug these into the previous equation and multiply by the denominator:

## Second Part

Therefore

From the first part,

Adding these two integrals,

Multiply both sides by the inverse of the last term and use