Inner product of x^p and x^q with weight x^2

[keddelove]

Hello, I am working on an assignment were I have shown that a certain equation defines an inner product, which was simple enough. Te equation was:

$$\left\langle {f,g} \right\rangle = \int\limits_0^1 {f\left( x \right)g\left( x \right)x^2 dx}$$My question then is: How do i state an equation for the inner product of x^p and x^q.

Sorry if the information is sparse

 

[matt grime]

You set f(x)=x^p and g(x)=x^q.

 

[HallsofIvy]

Looks straight forward to me. If
$$<f,g>= \int_0^1 f(x)g(x)x^2 dx$$
f(x)= x^p, and g(x)= x^q, then
$$<f,g>= \int_0^1 (x^p)(x^q)x^2dx= \int_0^1 x^{p+q+2}dx$$

 

[AKG]

Looks straight forward to me. If
$$<f,g>= \int_0^1 f(x)g(x)x^2 dx$$
f(x)= x^p, and g(x)= x^q, then
$$<f,g>= \int_0^1 (x^p)(x^q)x^2dx= \int_0^1 x^{p+q+2}dx$$

And you can give an exact number equal to that last expression.