(E) The average value is . The integral represents the area of
a trapezoid: . The average value is .
(B) Since x^2 + y 2 = 16 is a circle, the given integral equals the area of a
semicircle of radius 4.
(B) Use a graphing calculator.
(D) A vertical line at x = 2 divides the area under f into a trapezoid and a
triangle; hence, . Thus, the average value
of f on [0,6] is . There are points on f with y-values of in the
intervals [0,2] and [2,4].
(B)
(D) g′(x) = f(2x) · 2; thus g′(1) = f(2) · 2
(C) . (Why 14? See the solution
for Question 42.)
(C) This is the Mean Value Theorem for Integrals.
