from calculus we know that ,for any polynomial function f : R-R of degree <= n,the fuction of I(f) :R-R ,s----[tex]\int[/tex]f(u) du is a polynomial function of degree <=n+1
show that the map I: Pn--Pn+1 , f--I(f) is an injective linear transformation, determine a basis of the image of I and find the matrix M[tex]\in[/tex]M(n+2)*(n+1)(R) that represents I with respect to the basis 1,t,...t^n of Pn and the basis 1,t,...t^(n+1) of Pn+1
The Attempt at a Solution
can i use L(x+y)=L(x)+L(y) aL(x)=L(ax) to show linear transformation ? but for what value i can choose for x, y
for ''determine ...'' part i have no idea for it ,any help ?