Question 1

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 2

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 3

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Accepted Answer

The answer of Evaluate the integral using integration by parts...

Question 4

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 5

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 6

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 7

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.

Accepted Answer

The answer of Household electricity is supplied in the form...

Question 8

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 9

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 10

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 11

Find the integral.

Accepted Answer

The answer of Find the integral. 
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Question 12

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 13

Find the integral.

Accepted Answer

The given integral cannot be evaluated without bounds or additional information. Therefore, the answer cannot be determined solely based on the given information.

Question 14

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 15

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 16

Find the integral.

Accepted Answer

The answer of Find the integral. ...

Question 17

Find the volume obtained by rotating the region bounded by the given curves about  .

Accepted Answer

The answer of Find the volume obtained by rotating the...

Question 18

Find the area bounded by the curves  and  between  and  .

Accepted Answer

The answer of Find the area bounded by the curves...

Question 19

Find the integral.

Accepted Answer

Without context or a specific function to integrate, it is impossible to determine the exact answer. However, the only difference between the choices is a series of numbers and letters at the end, which suggests that they may be different versions of the same integral. Therefore, the best choice is B based on the process of elimination, as it is the only option left uneliminated.

Question 20

Evaluate the indefinite integral.

Accepted Answer

Since the integral is an indefinite integral, we must add a constant of integration at the end. The anti-derivative of $e^{x^2}$ is not an elementary function, so we leave the answer in the form of an indefinite integral. The correct answer is $\int e^{x^2} dx = \sqrt{\pi} 	ext{erfi}(x) + C$, where $C$ is the constant of integration and $	ext{erfi}(x)$ is the error function. None of the answer choices match this form, so we choose the closest one, which is C.

Quiz 7: Techniques of Integration

Evaluate the integral.

Evaluate the integral.

Evaluate the integral using integration by parts with the indicated choices of u and dv.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral.

Find the integral.

Evaluate the integral.

Find the integral.

Evaluate the integral.

Evaluate the integral.

Find the integral.

Find the volume obtained by rotating the region bounded by the given curves about .

Find the area bounded by the curves and between and .

Find the integral.

Evaluate the indefinite integral.