3. Let V = P3(Q) be a vector space of polynomials with coefficients in Q and variable x of degree at most 3. Let $ : V → Q is defined by ø(p(x)) = | *p(t)dt (a) Prove that ø is in the dual space of V....

Need assistance with this dual basis for linear algebra

Extracted text: 3. Let V = P3(Q) be a vector space of polynomials with coefficients in Q and variable x of degree at most 3. Let $ : V → Q is defined by ø(p(x)) = | *p(t)dt (a) Prove that ø is in the dual space of V. (b) Express ø as a linear combination of the dual basis.