MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Let f(x)=ax2+bx be a quadratic polynomial.
The following information about its average values is provided:
(i) Translate each of the above conditions into an algebraic equation in a and b.
(ii) Solve the simultaneous equations obtained in part (i) to determine the values of a and b.
(iii) Using the constants found, calculate the average value of f over the entire interval [0,4].