Consider the function k(u) = |u|.

a. Calculate ∫ 0

−2 k(u) du exactly. Hint: don’t use any integration methods to do this, just use some geometry and the formula for the area of a triangle.

b. Estimate ∫ 0

−2 k(u) du by using a right Riemann sum with four rectangles. Show that this right Riemann sum underestimates the actual area.

c. Estimate ∫ 0

−2 k(u) du by using a left Riemann sum with four rectangles. Show that this left Riemann sum overestimates the actual area.

d. Estimate ∫ 2 0 k(u) du by using a right Riemann sum with four rectangles. Show that this right Riemann sum overestimates the actual area.

e. Estimate ∫ 2 0 k(u) du by using a left Riemann sum with four rectangles. Show that this left Riemann sum underestimates the actual area.

f. Use a middle Riemann sum with 8 rectangles to estimate ∫ 2 −2 k(u) du. Compare your answer to the correct value of the integral. Can you explain your result?