chapter 5 – more review questions - wordpress.com · 2017. 1. 13. · calculus 12 & ap...
TRANSCRIPT
Calculus 12 & AP Calculus AB v2
1 of 4
Chapter 5 – More Review Questions First Name: _________________________ Last Name: _________________________ Block: ______ Part I: Multiple Choice. You may use your scientific calculator.
1. ∫ =+ dxxx 12
a)
Cxx +++ 1)1(31 22
b)
Cx ++131 2
c)
Cx ++121 2
d)
( ) Cx ++32 1
e)
1)1(21 22 ++ xx
2. Using the substitution xu cos= , ∫ ⋅20
cossinπ
dxxx is equivalent to
a) ∫− 20
π
duu b) ∫0
1duu c) ∫
1
0duu d) ∫
1
0sin duu e) ∫ 2
0
π
duu
Part II: Written Response. Show ALL your work in order to obtain full marks.
1. Find dxx
xx∫
+ 21
2 [2 marks]
2. Evaluate: ( )∫ ⋅ dxxx 2sin [2 marks]
Calculus 12 & AP Calculus AB v2
2 of 4
3. ( ) =−+∫ dxxx 132 [2 marks]
4. Evaluate: ∫1
03 dxx . Do not round the answer. [1 mark]
5. Evaluate: ∫ 40
sinπ
dxx [2 marks]
6. A particle moves along a line with velocity function 2)( 2 −−= tttv , where v is measured in
meters per second. a) Find the displacement of the particle during the time interval [1, 3] [ 1 mark]
b) Find the distance travelled by the particle during the time interval [1, 3]. [ 2 marks]
Calculus 12 & AP Calculus AB v2
3 of 4
7. The graph of the function f, consisting of three line segments, is shown below.
Let g(x) = ∫x
dttf3
)(
a) Compute g(-4). [1 mark] b) Compute g(8). [1 mark]
c) Find the absolute minimum value of g on the closed interval [-4, 8]? Justify your answer. [2 marks]
8. Let A be the area of the region that lies under the graph of 2)( xxf = from 10 ≤≤ x .
Using midpoints, approximate the area with 4 subintervals. Sketch the graph and the rectangles. Show your work and round to 3 decimals places. [2 marks]
Calculus 12 & AP Calculus AB v2
4 of 4
9. Draw a slope field for the following differential equation. Draw a particular function, y = f(x), that satisfies the initial condition f(0) = 1. Find the equation of the function.
ydxdy 2=