Question 1

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
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Question 2

Make the indicated substitution for an unspecified function  .  for

Accepted Answer

Since only one of the characters in the 11eaa88b_91e3_b0fb_a696_35f3fb5b0615_TB5869_11 string is different, we can compare the corresponding values in the two options. The only difference is in the 4th to last character, which is changing from 'c' to 'f'. Therefore, we should choose the option where the 4th to last character changes from 'c' to 'f', which is option C (11eaa88b_91e3_ff1f_a696_cf12f409d47a_TB5869_11)

Question 3

Use a computer or calculator to compute the Midpoint, Trapezoidal and Simpson's Rule approximation with  . Round to 4 decimal places.

Accepted Answer

The answer of Use a computer or calculator to compute...

Question 4

The location  of the center of gravity (balance point) of a flat plate bounded by  and the  -axis is given by  and  For the isosceles triangle bounded below by the  -axis and above by the function  (for  ), use symmetry to argue that  and  . Compute  .

Accepted Answer

The answer of The location  of the center of...

Question 5

Make the indicated substitution for an unspecified function  .  for

Accepted Answer

The answer of Make the indicated substitution for an unspecified...

Question 6

Evaluate the definite integral.

Accepted Answer

Without seeing the integral, it is impossible to determine the exact answer. However, the fact that all answer choices begin with the same string of characters (11eaa88b_91e1_8e0) suggests that the only difference between them is the final portion of the string, which is a unique identifier for each answer choice. The correct answer must depend on the integral itself, so we cannot determine the correct choice based solely on the provided strings.

Question 7

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
...

Question 8

Approximate the given value using Simpson's Rule with  . Round to 3 decimal places.

Accepted Answer

The answer of Approximate the given value using Simpson's Rule...

Question 9

Evaluate the indicated integral.

Accepted Answer

The answer of Evaluate the indicated integral. 
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Question 10

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
...

Question 11

Compute the Simpson's Rule approximation by hand for  . Round to 3 decimal places.

Accepted Answer

The answer of Compute the Simpson's Rule approximation by hand...

Question 12

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
...

Question 13

Evaluate the integral exactly.

Accepted Answer

The answer of Evaluate the integral exactly. 
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Question 14

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. 
...

Question 15

Compute the Trapezoidal Rule approximation by hand for  . Round to 3 decimal places.

Accepted Answer

The answer of Compute the Trapezoidal Rule approximation by hand...

Question 16

Evaluate the definite integral.

Accepted Answer

The answer of Evaluate the definite integral. 
...

Question 17

Estimate the integral numerically.

Accepted Answer

The answer of Estimate the integral numerically. 
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Question 18

Compute the error (the difference between the exact value and the approximation) in the Trapezoidal Rule approximation using  . Round to 5 decimal places.

Accepted Answer

The answer of Compute the error (the difference between the...

Question 19

Use a computer or calculator to compute the Simpson's Rule approximation with  . Round to 3 decimal places. Compare this value to the approximation given by your calculator.

Accepted Answer

The answer of Use a computer or calculator to compute...

Question 20

Evaluate the definite integral.

Accepted Answer

Without limits of integration, it is impossible to determine the exact value of the integral.

Quiz 5: Integration

Evaluate the integral.

Make the indicated substitution for an unspecified function . for

Use a computer or calculator to compute the Midpoint, Trapezoidal and Simpson's Rule approximation with . Round to 4 decimal places.

The location of the center of gravity (balance point) of a flat plate bounded by and the -axis is given by and For the isosceles triangle bounded below by the -axis and above by the function (for ), use symmetry to argue that and . Compute .

Make the indicated substitution for an unspecified function . for

Evaluate the definite integral.

Evaluate the integral.

Approximate the given value using Simpson's Rule with . Round to 3 decimal places.

Evaluate the indicated integral.

Evaluate the integral.

Compute the Simpson's Rule approximation by hand for . Round to 3 decimal places.

Evaluate the integral.

Evaluate the integral exactly.

Evaluate the integral.

Compute the Trapezoidal Rule approximation by hand for . Round to 3 decimal places.

Evaluate the definite integral.

Estimate the integral numerically.

Compute the error (the difference between the exact value and the approximation) in the Trapezoidal Rule approximation using . Round to 5 decimal places.

Use a computer or calculator to compute the Simpson's Rule approximation with . Round to 3 decimal places. Compare this value to the approximation given by your calculator.

Evaluate the definite integral.