1

-Findthe mo

s

t general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) =

1

2

+

4

5

x2 −

5

6

x

3

F(x) =

2-Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = (x + 3)(4x − 7)

F(x) =

3-Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = 3×1/4 − 5×3/4

F(x) =

4-Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) = 6x + 7×1.3

F(x) =

5-Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) =

4 | x3 |

+

3 |
x4 |

F(x) =

6-Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative.)

f(x) =

9

ex +

8

sec2 x

F(x) =

7-Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)

f ”(x) =

8

9

x8/9

f(x) =

8-Find the most general f. Use C for the constant of the first anti-derivative and D for the constant of the second anti-derivative.

f ”(x) = 6x + sin x

f(x) =

9-Find f.

f ‘(t) = 8 cos t + sec2t, −π/2 < t < π/2, f(π/3) = 4

f(t) =

10-Find f.

f

”(x) = 8 − 18x, f(0) = 6, f(2) = 16

f(x) =

11-A stone is dropped from the upper observation deck of a tower, 50 m above the ground. (Assume g = 9.8

m/s

2.)

(a) Find the distance (in meters) of the stone above ground level at time t.

h(t) =

(b) How long does it take the stone to reach the ground? (Round your answer to two decimal places.)

s

(c) With what velocity does it strike the ground? (Round your answer to one decimal place.)

m/s

(d) If the stone is thrown downward with a speed of 4 m/s, how long does it take to reach the ground? (Round your answer to two decimal places.)

s

12-A car is traveling at 116 km/h when the driver sees an accident 65 m ahead and slams on the brakes. What minimum constant deceleration is required to stop the car in time to avoid a pileup? (Round your answer to two decimal places.)

m/s2

13-Suppose f(x) > 0 on [2, 5]. If we use 3 rectangles, then (1)*f(2) + (1)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

True

False

14-Suppose f(x) > 0 on [2, 5].

(1.5)*f(2) + (1.5)*f(5) gives an estimate of the area under the graph of f.

True

False

15-Suppose f(x) > 0 on [2, 5].

(2)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

True

False