Conceptual questions Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. To evaluate - dx an appropriate trigonometric substitution is x = 5 sin(0). V25+x2 (Explain your reasoning)
Conceptual questions Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. To evaluate - dx an appropriate trigonometric substitution is x = 5 sin(0). V25+x2 (Explain your reasoning)
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Conceptual questions
Determine whether the statement is true or false. If it is true, explain why. If it is
false, explain why or give an example that disproves the statement.
1. To evaluate |
dx
an appropriate trigonometric substitution is x =5 sin(0).
V25+x2
(Explain your reasoning)
2. The Midpoint Rule is always more accurate than the Trapezoidal Rule. (Explain
your reasoning)
3. If fis a continuous, decreasing function on [1, 0) and lim f(x) = 0, then
00+x
S, f(x) dx is convergent. (Explain your reasoning)
4. If f(x) dx and g(x) dx are both divergent, then
S Ifx) + g(x) |dx is divergent. (Explain your reasoning)
5. What is the form of the partial fraction decomplex] Q and Q has only distinct
linear factors? What if a linear factor is repeated? What if has an irreducible
quadratic factor (not repeated)? What if the quadratic factor is repeated?
Problems
6. Evaluate the integral S( tan(x))? (cos(x))³ dx
7. Determine an appropriate trigonometric substitution. Apply the substitution to
transform the integral into a trigonometric integral. Do not evaluate the integral.
S dx
of 4
387 words
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![Aa v
12.5 v A A
Cambria
Paragraph
Styles
Dictate
X, X
evAv
I
U v ab
Conceptual questions
Determine whether the statement is true or false. If it is true, explain why. If it is
false, explain why or give an example that disproves the statement.
1. To evaluate |
dx
an appropriate trigonometric substitution is x =5 sin(0).
V25+x2
(Explain your reasoning)
2. The Midpoint Rule is always more accurate than the Trapezoidal Rule. (Explain
your reasoning)
3. If fis a continuous, decreasing function on [1, 0) and lim f(x) = 0, then
00+x
S, f(x) dx is convergent. (Explain your reasoning)
4. If f(x) dx and g(x) dx are both divergent, then
S Ifx) + g(x) |dx is divergent. (Explain your reasoning)
5. What is the form of the partial fraction decomplex] Q and Q has only distinct
linear factors? What if a linear factor is repeated? What if has an irreducible
quadratic factor (not repeated)? What if the quadratic factor is repeated?
Problems
6. Evaluate the integral S( tan(x))? (cos(x))³ dx
7. Determine an appropriate trigonometric substitution. Apply the substitution to
transform the integral into a trigonometric integral. Do not evaluate the integral.
S dx
of 4
387 words
E Focus](https://content.bartleby.com/qna-images/question/4cca4514-bc37-4dde-8bb8-3d7297fd525b/c175ff74-5949-44c7-9b86-44fbc58c9989/1ku1bie_processed.jpeg)
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