Let f(x)=14πx^2 and g(x)=k^2 sin(πx/2k) for k>0.?

Question

a. Find the average value of f on [1,4]

b. For what value of k will the average value of g on [0,k] be equal to the average vaslue of f on [1,4]?

Answer 1

a. Just integrate f(x) on the interval [1,4] and then divide this number by 3.
b. Next, integrate g(x) on the interval [0,k] and set this equal to the answer from part a and solve for k.