Calculus help :)

Question

Water flows into and out of a storage tank. A graph of the rate of change r(t)

 of the volume of water in the tank, in liters per day, is shown.

If the amount of water in the tank at time t = 0

 is 35,000 L, use the Midpoint Rule to estimate the amount of water (in L) in the tank four days later. (Let n = 4.)

Answer 1

The amount of water is the integral of the rate of change + the initial amount.

To find the integral, break the 4 days into 4 equal pieces, so 4 rectangle, each 1 day wide. Use the midpoint of each of those rectangles as the height of the rectangle and the width is "1".

Area of rectangle #1 (from t = 0 to t = 1): 1500(1) = 1500

Area of rectangle #2 (from t = 1 to t = 2): 1800(1) = 1800

Area of rectangle #3 (from t = 2 to t = 3): 750(1) = 750

Area of rectangle #4 (from t = 3 to t = 4): -700(1) = -700

Total area = 1500 + 1800 + 750 + -700 = 3350

So the amount of water is 35000 + 3350