De Anza College Compute the Values Calculus Questions

Description

Finish it on paper or on pdf and send me back, if use hand writing, please write it clearly

WORKSHEET No.16
Due on May 23 (11:59pm)
Name:
Student ID#:
Let 𝑓(𝑥) be a function described by the following table.
𝑥
𝑓(𝑥)
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 𝑓(𝑥) is increasing and concave up for 2.0 ≤ 𝑥 ≤ 2.6.
1.2
(a) Find the approximation 𝑻𝟑 (Trapezoidal Rule, 3 subintervals, 𝑛 = 3) for ∫1.3 𝑓 (𝑥)𝑑𝑥.
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 ∫1.3 𝑓(𝑥 )𝑑𝑥 ?
1.2
(c) Find the approximation 𝑺𝟔 (Simpson’s Rule, 6 subintervals, 𝑛 = 6) for ∫1.3 𝑓 (𝑥 )𝑑𝑥.
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 “P” if the
integral is proper or write “I” if it is improper.
(0.5 pts each)
(a)
ò
¥
5
dx
(x – 2) 2
(b)
ò
5
2
dx
(x – 2) 2
(a)
(b)
(c)
ò
5
3
dx
(x – 2) 2
(c)
2. 2. Determine if the improper integral converges or diverges. In the box, write “C” if the
improper integral is convergent or write “D” if it is divergent.
(Hint: Use Comparison Test.)
(0.5 pts each)
(a)
¥
x5
ò2 x 6 – 1dx
¥
(c)
ò2
(e)
ò4
(g)
ò2
dz
z3 +1
¥ 3 + sin
¥
(b)
x
x
dx
x3 +1
¥
ò2
( x 4 + 4 x + 1) 2
¥
(d)
ò1
(f)
ò1
dx
dx
( x + 5) 5
¥ 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
∫
2
ò
3
x
ò 1 + x2 dx
4
òx
5
x2
ò 1 + x 2 dx
6
3 x
x
ò e dx
7
x
xe
ò dx
1
1+ x
2
dx
2
2
8
9
10
3x − 8
dx
2
+x
∫x

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