is the sum of the areas of two triangles: .(C) Because is a semicircle of radius 8, its area is 32π. The
domain is [−8,8], or 16 units wide. Hence the average height of the
function is .(C) The average value is equal to .(C) The average value is equal to .(C) From the integral, we get a = 1, b = 5, so and . Replace x with xk and replace dx with Δx in the
integrand to get the general term in the summation.
(D) From the integral, we get a = 0, b = π, so and . Replace x with xk and replace dx with Δx in the
integrand to get the general term in the summation.
(B) From the Riemann Sum, we see , then . Notice that
the term involving k in the Riemann Sum is not equal to but .
Thus, we choose , so a = 0 and , so b = 3. Since xk
replaces x, f(x) = sin(2x + 2) giving the integral .