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
