Download Ch 6 Test Review

AP Calculus
Ch 6 Test Review
I. Try the indicated text book problems on pages 325- 326:
4, 8, 12, 14, 20, 22, 38, 44, 52, 58, 70
II. f(x) = -x2 + 4x
a) Estimate the area between f(x) and the x-axis on [1,4].
b)
. Determine F(x).
c) Evaluate
.
d) Find F(x) that passes through (0, -3).
e) Write F(6) – F(1) using notation from the First Fundamental Theorem.
III.
a) What is the difference between F(x) and
b) Given
?
and F(x1) = 5, determine F(x2).
IV. Try the following AP exam questions:
1. f(x) and g(x) are differentiable functions of x such that
a.
b.
d.
e.
2. If f ’(x)=x3 + 4x and f(0)= 2, then f(x) is
a. 3x2+4
b. x3 +4x +4
d. 1/4x4 +2x2 + 2
e. x4/4 + 2x2 + 4
, then
c.
c. x4 + 4x + 2
3. What is the area bounded by x3, the x-axis, x=1 and x=2?
a. 7/3
b. 1
c. 15/4
d. 7
e. 9
4.
6
0
1
The graph of df/dx is given. If f(0) = 5, the f(1)=
a. 0
b. 3
c.6
d. 8
e. 11
SOLUTIONS:
I.
II.
4. 2t2 + ln t + C
8. X3/3 + 3x2 + 9x +C
12. 2/5 x 5/2 -2 ln x + C
14. 2x/(ln 2) + C
20. 3sin t + 2t3/2 + C
22. 2 ln x – πcos x + C
3
2
38. 2x + 4x + 5x  94
44. Area under y on [0,1]=2, area under y on [1,3]=20, so area under y on [0,3]= 22.
52. t3/3 – 14t2 + 49t  93 cu m
58. X1 is relative min, x2 is inflection point, x3 is relative max, between x3 and x4 is an inflection
point.
70. A is antiderivative of f, B is f, and C is the derivative of f.
a. 9
b. –x3/3 + 2x2 + C
c. 7/3 +2/3 = 3
d. –x3/3 + 2x2 – 3
e.
III
a. F(x) is an indefinite integral. It is an antiderivitive of f(x) and produces a family of curves.
is a definite integral which can be evaluated.
b. F(x2) – F(x1) =
IV.
1. A
2. D
. F(x2) – 5 = -2. F(x2) =3
3. C
4. D