1. No category

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
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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.
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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