Let J: P(R) W where WC P (R) and where J is the integration operator...

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Let J: P₁(R) → W where WC P₂ (R) and where J is the integration operator such that J(p) = [ p(x)dx with the constant term of the anti-derivative equal to zero. In other words, J(p) (0) = 0. This is another way of writing J(p) = 0 when x = 0. Write a general formula for J (p) for an arbitrary polynomial p € P₁ (R). Let J: P₁(R) → W where WC P₂ (R) and where J is the integration operator such that J(p) = [ p(x)dx with the constant term of the anti-derivative equal to zero. In other words, J(p) (0) = 0. This is another way of writing J(p) = 0 when x = 0. Write a general formula for J (p) for an arbitrary polynomial p € P₁ (R).

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Let px be an arbitrary polynomial of degree n in PR Then we can write ... View the full answer