Calculus 12 & AP Calculus AB v2

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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

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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

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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

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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=