- #1

Lelouch

- 18

- 0

## Homework Statement

## Homework Equations

I am not sure. I have not seen the triangle inequality for inner products, nor the Cauchy-Schwarz Inequality for the inner product. The only thing that my lecture notes and textbook show is the axioms for general inner products, the definition of norm (length) and distance between inner product. And some basic consequences of the inner product axioms for norm and distance, s.t. norm is greater equal to 0, norm multiplied by a constant, symmetry of distance, and distance is greater than or equal to 0.

The rest are examples of inner products i.e. on ##R^n##.

## The Attempt at a Solution

I have solved the definite integral for the given ##p(x)## and ##q(x)## which has the value ##\frac{68}{21}##.

What I thought I need to show is that ##<p, q> \leq <p> + <q>## for the triangle inequality. But this seems nonsensical to me since the inner product is defined for two vectors and not for one.

Maybe I have to show ##<p, q> \leq <p, p> + <q, q>##? But at this point I am just guessing since I do not know the triangle inequality for inner products nor the Cauchy-Schwarz inequality for inner products.