# Integration - Quiz 1

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| By Siti Aisyah
S
Siti Aisyah
Community Contributor
Quizzes Created: 1 | Total Attempts: 268
Questions: 20 | Attempts: 272

Settings

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• 1.
B.
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D.
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A.
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C.
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B.
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D.
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A.
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4

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3

B.
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18

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19

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20

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21

D. 21
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### Find the area of the shaded region.

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20 area units

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area units

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21 area units

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area units

D.  area units
• 11.

### Find the area of the region bounded by the graphs of , y-axis,  y = 1 and y = 5 lines.

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• B.

area units

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6 area units

• D.

10 area units

A.
Explanation
To find the area of the region bounded by the graphs of y-axis, y = 1, and y = 5 lines, we need to find the area between the y = 1 and y = 5 lines. Since the region is bounded by the y-axis, the x-values will range from 0 to a certain value. To find this value, we need to find the x-intercept of the line y = 5. The x-intercept is where y = 0, so substituting y = 0 into the equation y = 5 gives us x = 0. Therefore, the x-values range from 0 to 0. The area of the region is then given by the formula A = (5-1) * (0-0) = 0. Thus, the area of the region bounded by the graphs is 0 area units.

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• 12.

### Find the area under the curve  from x = 0 to x = 4

• A.

64 area units

• B.

80 area units

• C.

96 area units

• D.

108 area units

B.  80 area units
Explanation
The area under the curve from x = 0 to x = 4 is equal to the integral of the function over that interval. Without knowing the specific function, it is not possible to calculate the exact area. Therefore, the given answer of "80 area units" is a possible area under the curve, but it cannot be confirmed as the correct answer without further information.

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• 13.

### Find the volume of the solid figure generated by rotating the area bounded by , y-axis, y = 0 and y = 2.

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• B.

• C.

• D.

D.
Explanation
To find the volume of the solid figure generated by rotating the area bounded by the y-axis, y = 0, and y = 2, we can use the method of cylindrical shells. Since the area is bounded by the y-axis and two horizontal lines, we can consider a vertical strip of width dx at a distance x from the y-axis. The height of this strip will be 2, and the circumference will be 2πx. Therefore, the volume of this strip will be 2πx * 2 * dx = 4πx dx. Integrating this expression from x = 0 to x = 2, we can find the total volume of the solid figure.

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• 14.

### Find the area enclosed between the curves  and  .

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area units

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area units

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area units

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area units

A.  area units
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D.
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Undefined

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B.
• 17.

### This following improper integral has a finite value. Find its value.

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0

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1

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2

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Undefined

C. 2
Explanation
The given improper integral is not properly stated in the question, so it is difficult to provide a clear explanation. However, based on the answer provided, it can be inferred that the integral is convergent and evaluates to a finite value of 2. Without further information, it is not possible to determine the specific function or limits of integration involved in the integral.

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• 18.

### Integration is essentially the same as ..........

• A.

Differentiation

• B.

Antidifferentiation

B. Antidifferentiation
Explanation
Integration is essentially the same as antidifferentiation. Integration involves finding the antiderivative of a function, which is the reverse process of differentiation. Antidifferentiation allows us to find the original function when only its derivative is known. Therefore, integration and antidifferentiation are synonymous terms in calculus.

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• 19.

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A

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B

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C

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D

B. B
• 20.

### The definite integral for a function that is below the x-axis is always positive. Is that true or false?

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True

• B.

False

B. False
Explanation
The definite integral for a function that is below the x-axis is not always positive. The value of the definite integral represents the signed area between the function and the x-axis. If the function is below the x-axis, the area will be negative. Therefore, the statement is false.

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