Quiz 4 Question 1 1 / 1 point

Use the Table of Integrals to evaluate the integral.

Select the correct answer.

Question 2 1 / 1 point

Use the Trapezoidal Rule to approximate

for n = 4.

Select the correct answer. The choices are rounded to four decimal places.

2.3792

2.3742

2.4792

2.4002

2.3797

2.378

Question 3 1 / 1 point

Which of the following integrals are improper?

Select the correct answers.

Question 4 1 / 1 point

Evaluate the integral

Select the correct answer.

Question 5 1 / 1 point

Evaluate the integral

Select the correct answer.

Question 6 1 / 1 point

Evaluate the integral

Select the correct answer.

Question 7 1 / 1 point

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

Select the correct answer.

Question 8 1 / 1 point

Find the area under the curve

from x = 1 to x = t. Evaluate it for t = 10, 100, and 1000 in order to find the total area under the

curve for

Select the correct answer. The choices give the total area only.

Area = 360

Area = 36

Area = 72

Question 9 1 / 1 point

The intensity of light with wavelength traveling through a diffraction grating with N slits at an

angle is given by where and d is the distance between

adjacent slits. A helium-neon laser with wavelength is emitting a narrow

band of light, given by through a grating with 1,500 slits spaced 0.0001 m

apart. Use the Midpoint Rule with n = 10 to estimate the total light intensity emerging from the grating. Round the result to the nearest thousandth.

Select the correct answer.

4.813

3.252

4.262

4.374

4.363

4.263

Question 10 1 / 1 point

The left, right, Trapezoidal, and Midpoint Rule approximations were used to estimate where f is the function whose graph is shown. The estimates were 0.3125, 0.6444, 0.2709, and 0.5241, and the same number of subintervals were used in each case.

Choose the correct statement.

Question 1 1 / 1 point

Determine whether the following integral is convergent or divergent.

Select the correct answer.

integral is convergent

integral is divergent

Question 2 1 / 1 point

Use the Table of Integrals to evaluate the integral.

Select the correct answer.

Question 3 1 / 1 point

Estimate the area of the shaded region in the graph by using the Trapezoidal Rule with n=4.

Select the correct answer.

12

10.5

6.9

8.5

7.4

12.5

Question 4 1 / 1 point

Use the Table of Integrals to evaluate the integral.

Select the correct answer.

Question 5 1 / 1 point

Evaluate the integral

Select the correct answer.

Question 6 1 / 1 point

The approximation for the integral is 14,689.556579 with n = 10. It was calculated using which rule?

Select the correct answer.

Trapezoidal Rule

Simpson's Rule

Midpoint Rule

Question 7 1 / 1 point

The figure shows a pendulum with length L that makes a maximum angle with the vertical. Using Newton's Second Law it can be shown that the period T (the time for one complete swing) is given by

where and g = 9.8 is the acceleration due to gravity. If L = 5 and

use Simpson's Rule with n = 10 to find the period T. Round the result to the nearest thousandth.

4.893 s

5.404 s

5.243 s

4.64 s

4.693 s

3.682 s

Question 8 1 / 1 point

Use the Midpoint Rule to approximate the given integral with the specified value of n. Compare your result to the actual value and find the error in the approximation.

, n = 6.

Choose the correct answer from below. The choices give the error only.

-0.00496

-0.00016

0.00014

0.00004

0.10004

-0.00096

Question 9 1 / 1 point

Use the Table of Integrals to evaluate the integral.

Select the correct answer.

Question 10 1 / 1 point

Evaluate the integral

Select the correct answer.