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WORKSHEET No.16

Due on May 23 (11:59pm)

Name:

Student ID#:

Let π(π₯) be a function described by the following table.

π₯

π(π₯)

2.0

2.3

2.1

2.4

2.2

2.6

2.3

2.9

2.4

3.3

2.5

3.8

2.6

4.4

Suppose also that π(π₯) is increasing and concave up for 2.0 β€ π₯ β€ 2.6.

1.2

(a) Find the approximation π»π (Trapezoidal Rule, 3 subintervals, π = 3) for β«1.3 π (π₯)ππ₯.

Show all your work and round your answer to two decimal places.

1.2

(b) Is your answer in part(a) greater than or less than the actual value of β«1.3 π(π₯ )ππ₯ ?

1.2

(c) Find the approximation πΊπ (Simpsonβs Rule, 6 subintervals, π = 6) for β«1.3 π (π₯ )ππ₯.

Show all your work and round your answer to two decimal places.

WORKSHEET No.17

Due on May 23 (11:59pm)

Name:

Student ID#:

You do not have to show your work.

1. Classify each of the integrals as proper or improper integrals. In the box, write βPβ if the

integral is proper or write βIβ if it is improper.

(0.5 pts each)

(a)

Γ²

Β₯

5

dx

(x – 2) 2

(b)

Γ²

5

2

dx

(x – 2) 2

(a)

(b)

(c)

Γ²

5

3

dx

(x – 2) 2

(c)

2. 2. Determine if the improper integral converges or diverges. In the box, write βCβ if the

improper integral is convergent or write βDβ if it is divergent.

(Hint: Use Comparison Test.)

(0.5 pts each)

(a)

Β₯

x5

Γ²2 x 6 – 1dx

Β₯

(c)

Γ²2

(e)

Γ²4

(g)

Γ²2

dz

z3 +1

Β₯ 3 + sin

Β₯

(b)

x

x

dx

x3 +1

Β₯

Γ²2

( x 4 + 4 x + 1) 2

Β₯

(d)

Γ²1

(f)

Γ²1

dx

dx

( x + 5) 5

Β₯ 3 + sin x

x

dx

5

dx

e10t + 51

(a)

(b)

(c)

(d)

(e)

(f)

(g)

WORKSHEET No.15

Due on May 23 (11:59pm)

Name:

Student ID#:

In each integral, determine which of the following techniques are most useful to

evaluate the integral. Find the technique (or method) that you need to use as the first

step. Write one letter in the box. Do not evaluate it. You do not have to show your work.

(0.5 pts each)

A) U Substitution

B) Integration by parts

C) Complete the square

D) Partial fractions

E) Long division

F) Trig substitution

Example

A

x 2 + 2x + 3

dx

x +1

1

dx

x2 – 5x + 6

1

β«

2

Γ²

3

x

Γ² 1 + x2 dx

4

Γ²x

5

x2

Γ² 1 + x 2 dx

6

3 x

x

Γ² e dx

7

x

xe

Γ² dx

1

1+ x

2

dx

2

2

8

9

10

3x β 8

dx

2

+x

β«x

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