CALCULUS WORKSHEET 1 ON FUNDAMENTAL THEOREM OF CALCULUS Do Not Use Calculator on 1 and 2. Work the following on notebook paper. Work problems 1 - 3 by both methods. 1 1. y 2 2 and y 1 6. Find y 3 . x 2. f x 2 cos x and f 0 3. Find f . 4 _____________________________________________________________________________ Work problems 3– 6 using the Fundamental Theorem of Calculus and your calculator. dW 1 dW 3. Water flows into a tank at a rate of is measured in 600 20t t 2 , where dt 75 dt gallons per hour and t is measured in hours. If there are 150 gallons of water in the tank at time t = 0, how many gallons of water are in the tank when t = 24? 4. f x cos x3 and f 0 2. Find f 1 . 5. f x e x and f 5 1. Find f 2 . 2 6. A particle moving along the x-axis has position x t at time t with the velocity of the particle v t 5sin t 2 . At time t = 6, the particle’s position is (4, 0). Find the position of the particle when t = 7. ________________________________________________________________________________ Use the Fundamental Theorem of Calculus and the given graph. 7. The graph of f is shown on the right. y 1 f x dx 6.2 4 and f 1 3. Find f 4 . x 1 4 8. The graph of f is the semicircle show on the right. Find f 4 given that f 4 7. y x -4 9. The graph of g is shown on the right. Find g 5 given that g 1 8. 4 y x Answers 32 1. 3 2. 2 3 3. 357.36 gallons 4. 2.932 7. 9.2 5. 0.996 6. 3.837 9. 22 8. 7 8
© Copyright 2025