Question 1

Evaluate the integral using integration by parts with the indicated choices of u and dv.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E)

Accepted Answer

In order to use integration by parts, we need to choose u and dv. We want to make a choice that simplifies the integral after applying the rule.

Let u be ln(x) and dv be dx/(x^2+1). Then, du/dx=1/x and v=arctan(x).

Using the formula for integration by parts, we have:

∫ ln(x) dx/(x^2+1) dx = ln(x) arctan(x) - ∫ (arctan(x)/x) dx

The second term on the right-hand side can be integrated using integration by substitution with u = arctan(x), du/dx = 1/(1+x^2), and dv = dx/x. This gives us:

∫ (arctan(x)/x) dx = (1/2) arctan^2(x) + C

Therefore, the final answer is:

∫ ln(x) dx/(x^2+1) dx = ln(x) arctan(x) - (1/2) arctan^2(x) + C

Choice (C) is the best choice because it gives us u and dv that simplify the integral when applying the rule of integration by parts.

Question 2

Evaluate the integral.  &#10;A) 6.5700&#10;B)  &#10;C) None of these&#10;D) 0.7166&#10;E) 11.8665

Accepted Answer

11ea8a3b_b6f7_11c6_9fff_db91c93f6837_TB6897_11

Question 3

Find the integral.  &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

11ea8a3b_b6f7_8601_9fff_41ddf1428724_TB6897_11

Question 4

Evaluate the integral.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) None of these

Accepted Answer

The answer of Evaluate the integral.  &#10;A)  &#10;B)...

Question 5

Evaluate the indefinite integral.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) None of these

Accepted Answer

The answer of Evaluate the indefinite integral.  &#10;A) ...

Question 6

Evaluate the integral.  &#10;

Accepted Answer

The answer of Evaluate the integral.  &#10;...

Question 7

Evaluate the following integral.  &#10;

Accepted Answer

The answer of Evaluate the following integral.  &#10;...

Question 8

Find the integral.  &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Find the integral.  &#10;A)  &#10;B)...

Question 9

Evaluate the integral.  &#10;A)  &#10;B)  &#10;C)  &#10;D)  &#10;E) None of these

Accepted Answer

The answer of Evaluate the integral.  &#10;A)  &#10;B)...

Deck 6: Extension A: Applications of Integration