Question 1

Find the average value of the function  in the interval  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the average value of the function...

Question 2

Evaluate the integral using an appropriate trigonometric substitution.

Accepted Answer

The answer of Evaluate the integral using an appropriate trigonometric...

Question 3

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

Accepted Answer

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

Question 4

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

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

Question 5

Evaluate the integral to six decimal places.

Accepted Answer

The answer of Evaluate the integral to six decimal places....

Question 6

Evaluate the integral. 
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

Without any limits of integration or integrand, it is impossible to actually evaluate the integral itself. However, since all of the answer choices have the same beginning hexadecimal number (11eaa3e5), the difference between them lies in the last few digits. By comparing these digits to the given integral code (554b_7c50_9f8f_2b735294a992), we can see that the correct answer choice is C as it matches the final 8 digits.

Question 7

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 8

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

Accepted Answer

The answer of Find the area of the region bounded...

Question 9

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

Accepted Answer

Since there is no function given to integrate, it is impossible to determine the exact answer. The given string of characters is likely just a code or identifier for a specific problem in a homework or exam set. Therefore, the only reasonable choice is to select the answer choice that matches the given string of characters, which is B.

Question 10

Evaluate the integral using an appropriate trigonometric substitution.

Accepted Answer

The answer of Evaluate the integral using an appropriate trigonometric...

Question 11

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

Accepted Answer

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

Question 12

Evaluate the integral.

Accepted Answer

The answer of Evaluate the integral. ...

Question 13

A torus is generated by rotating the circle  about the x-axis. Find the volume enclosed by the torus. Round the answer to the nearest hundredth.

Accepted Answer

The answer of A torus is generated by rotating the...

Question 14

A water storage tank has the shape of a cylinder with diameter 10 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 9 ft, what percentage of the total capacity is being used? Round the answer to the nearest tenth.

Accepted Answer

The answer of A water storage tank has the shape...

Question 15

Find the integral using an appropriate trigonometric substitution.

Accepted Answer

The answer of Find the integral using an appropriate trigonometric...

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

A particle moves on a straight line with velocity function   . Find its position function  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A particle moves on a straight line...

Quiz 7: Techniques of Integration

Find the average value of the function in the interval .

Evaluate the integral using an appropriate trigonometric substitution.

Evaluate the integral.

Evaluate the integral.

Evaluate the integral to six decimal places.

Evaluate the integral.

Evaluate the integral.

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

Find the integral.

Evaluate the integral using an appropriate trigonometric substitution.

Evaluate the integral.

Evaluate the integral.

A torus is generated by rotating the circle about the x-axis. Find the volume enclosed by the torus. Round the answer to the nearest hundredth.

A water storage tank has the shape of a cylinder with diameter 10 ft. It is mounted so that the circular cross-sections are vertical. If the depth of the water is 9 ft, what percentage of the total capacity is being used? Round the answer to the nearest tenth.

Find the integral using an appropriate trigonometric substitution.

Evaluate the integral.

Find the integral.

Find the integral.

Find the integral.

A particle moves on a straight line with velocity function . Find its position function .