Question

Consider the weighted inner product defined by(f,g) = ∫¹－₁ f(x)g(x) / 1+x² dx for functions f and g. The module midterm contains a function integral that accepts a function f, and two values a and b, and computes an approximation of the value ∫b,a f(x)dx Use integral to define a function inner product that accepts two functions fand g and returns the value ⟨f,g⟩ defined above.

Answer 1

To define the inner product using the weighted inner product formula, we can use the 'integral' function to approximate the value of ∫b,a f(x)dx. The inner product is defined as ⟨f,g⟩ = ∫¹－₁ f(x)g(x) / (1+x²) dx. We can define a function 'inner_product' that takes two functions f and g and returns the value of the inner product by calling the 'integral' function with the functions f and g and the limits of integration a and b.

Step-by-step explanation:

To define the inner product using the weighted inner product formula, we can use the 'integral' function to approximate the value of ∫b,a f(x)dx.

The inner product is defined as ⟨f,g⟩ = ∫¹－₁ f(x)g(x) / (1+x²) dx.

We can define a function 'inner_product' that takes two functions f and g and returns the value of the inner product by calling the 'integral' function with the functions f and g and the limits of integration a and b.