Question 1

Find the integral. 
A) 
B) 
C) 
D)

Accepted Answer

D

Question 2

Find the integral. 
A) 
B) 
C) 
D)

Accepted Answer

D

Question 3

Use a table of integrals to evaluate the integral. 
A) 
B) 
C) 
D)

Accepted Answer

A

Question 4

Use the Table of Integrals to evaluate the integral. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the Table of Integrals to evaluate...

Question 5

Determine whether the improper integral converges or diverges,and if it converges,find its value. 
A) 
B) 
C) 15
D) Diverges

Accepted Answer

The answer of Determine whether the improper integral converges or...

Question 6

Find the integral. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the integral. 
A) 
B) 
C) 
D)...

Question 7

Determine whether the improper integral converges or diverges,and if it converges,find its value. 
A) 
B) 0
C) 
D) Diverges

Accepted Answer

We have to determine the convergence of the improper integral:

$\int_{0}^{1} \frac{\ln x }{\sqrt{x}}dx$

We can use integration by substitution to solve it. Let $t=\sqrt{x}$. Then, $x=t^2$ and $dx=2tdt$. Also, the limits of integration change as:

$x=0$ $\Rightarrow$ $t=0$

$x=1$ $\Rightarrow$ $t=1$

Substituting these in the integral and simplifying, we obtain:

$\int_{0}^{1} \frac{\ln x }{\sqrt{x}}dx=\int_{0}^{1} 2\ln t dt=-\Big[2t \ln t - 2t\Big]_{0}^{1}=2$

Therefore, the integral converges and its value is 2. The correct choice is (C).

Question 8

Determine whether the improper integral converges or diverges,and if it converges,find its value. 
A) 3
B) 6
C) 0
D) Diverges

Accepted Answer

The answer of Determine whether the improper integral converges or...

Question 9

Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth.

Accepted Answer

The answer of Estimate the area of the shaded region...

Question 10

Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true? 
A) 
B) 
C) 
D) 
E) none of these

Accepted Answer

The answer of Let a and b be real numbers.What...

Question 11

Use the Table of Integrals to evaluate the integral.

Accepted Answer

The answer of Use the Table of Integrals to evaluate...

Question 12

Evaluate the integral or show that it is divergent.

Accepted Answer

The answer of Evaluate the integral or show that it...

Question 13

Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The Midpoint Rule for approximating an integral is given by:
$\int_a^bf(x)dx\approx(b-a)f\left(\dfrac{a+b}{2}\right)$
In this case, we have:
$\int_0^2\sqrt{1+x^2}dx\approx(2-0)\sqrt{1+(0.5)^2}=2\sqrt{1.25}\approx 2.2361$
The closest option is D) 11eaae29_f4d7_63e6_87fe_41ee976000c1_TB2067_11, which is equal to 2.2361. Therefore, D is the best choice.

Question 14

Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants. 
A) 
B) 
C) 
D)

Accepted Answer

The form of a partial fraction decomposition of a rational expression consists of a sum of terms, where each term has a constant numerator and a linear or quadratic denominator. The numerator may be a constant or a linear polynomial. The denominator may have repeated factors, irreducible quadratic factors, or both. The form of the partial fraction decomposition in choice B is the correct format, with constants represented by hexadecimal digits.

Question 15

Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.) 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the Midpoint Rule to approximate the...

Question 16

A manufacturer of light bulbs wants to produce bulbs that last about 400 hours but,of course,some bulbs burn out faster than others.Let F(t) be the fraction of the company's bulbs that burn out before t hours. F(t) lies between 0 and 1. Let  .What is the value of  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A manufacturer of light bulbs wants to...

Question 17

Make a substitution to express the integrand as a rational function and then evaluate the integral.  Round the answer to four decimal places.

Accepted Answer

The answer of Make a substitution to express the integrand...

Question 18

Use the Table of Integrals to evaluate the integral to three decimal places.

Accepted Answer

The answer of Use the Table of Integrals to evaluate...

Question 19

Find the integral. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the integral. 
A) 
B) 
C) 
D)...

Question 20

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Quiz 6: Techniques of Integration

Find the integral.

Find the integral.

Use a table of integrals to evaluate the integral.

Use the Table of Integrals to evaluate the integral.

Determine whether the improper integral converges or diverges,and if it converges,find its value.

Find the integral.

Determine whether the improper integral converges or diverges,and if it converges,find its value.

Determine whether the improper integral converges or diverges,and if it converges,find its value.

Estimate the area of the shaded region by using the Trapezoidal Rule with n = 4.Round the answer to the nearest tenth.

Let a and b be real numbers.What integral must appear in place of the question mark "?" to make the following statement true?

Use the Table of Integrals to evaluate the integral.

Evaluate the integral or show that it is divergent.

Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)

Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants. $Write the form of the partial fraction decomposition of the rational expression.Do not find the numerical values of the constants. A) B) C) D)$

Use the Midpoint Rule to approximate the given integral with the specified value of n .(Round your answers to four decimal places.)

Make a substitution to express the integrand as a rational function and then evaluate the integral. Round the answer to four decimal places.

Use the Table of Integrals to evaluate the integral to three decimal places.

Find the integral.

Evaluate the integral.