Quiz 6: Techniques of Integration

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

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

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

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)

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

Evaluate the integral or show that it is divergent.

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

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

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places. A)2.0076 B)2.6098 C)2.9504 D)2.2955

Use Simpson's Rule to approximate the integral with answers rounded to four decimal places. A)3.6993 B)2.9599 C)4.0689 D)3.3296

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

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

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

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

Use the Table of Integrals to evaluate the integral.

Evaluate the integral.

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)

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

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

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

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

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

Find the integral.

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

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

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

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

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

Evaluate the integral. A) B) C) D) E)

A particle moves on a straight line with velocity function  . Find its position function . A) B) C) D) E)

Evaluate the integral using the indicated trigonometric substitution. A) B) C) D) E)

Find the integral using an appropriate trigonometric substitution. A) B) C) D)

Find the integral using an appropriate trigonometric substitution. A) B) C) D)

Household electricity is supplied in the form of alternating current that varies from 170 V to -170 V with a frequency of 60 cycles per second (Hz). The voltage is thus given by the function E(t), where t is the time in seconds. Voltmeters read the RMS (root-mean-square) voltage, which is the square root of the average value of over one cycle. Calculate the RMS voltage of household current. Round your answer to the nearest integer.

Evaluate the integral using the indicated trigonometric substitution.

Find the area of the region bounded by the hyperbola and the line .

Find the integral.

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

Evaluate the indefinite integral. A) B) C) D) E)

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

Evaluate the integral. A) B) C) D) E)

Evaluate the integral. A)6.5700 B) C) D)0.7166 E)11.8665

Evaluate the integral. A) B) C) D) E)

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

Evaluate the integral.

Evaluate the following integral.