Q. What is the integral of e^x dx?
-
A.
e^x + C
-
B.
e^x
-
C.
x e^x + C
-
D.
x e^x
Solution
The integral of e^x is e^x + C, where C is the constant of integration.
Correct Answer:
A
— e^x + C
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Q. What is the integral of e^x with respect to x? (2023)
-
A.
e^x + C
-
B.
xe^x + C
-
C.
e^x/x + C
-
D.
x^2e^x + C
Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the integral of e^x? (2023)
-
A.
e^x + C
-
B.
xe^x + C
-
C.
e^x/x + C
-
D.
x^2e^x + C
Solution
The integral of e^x is e^x + C.
Correct Answer:
A
— e^x + C
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Q. What is the integral of f(x) = 1/x? (2023)
-
A.
ln
-
B.
x
-
C.
+ C
-
D.
1/x + C
-
.
x + C
-
.
e^x + C
Solution
The integral of 1/x is ln|x| + C.
Correct Answer:
A
— ln
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Q. What is the integral of f(x) = 2x from 0 to 3?
Solution
∫(2x)dx from 0 to 3 = [x^2] from 0 to 3 = 9 - 0 = 9.
Correct Answer:
B
— 6
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Q. What is the integral of f(x) = 2x with respect to x?
-
A.
x^2 + C
-
B.
2x^2 + C
-
C.
x^2 + 2C
-
D.
2x + C
Solution
The integral ∫2x dx = x^2 + C.
Correct Answer:
A
— x^2 + C
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Q. What is the integral of f(x) = 2x?
-
A.
x^2 + C
-
B.
2x^2 + C
-
C.
x^2 + 2C
-
D.
2x + C
Solution
∫2x dx = x^2 + C.
Correct Answer:
A
— x^2 + C
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Q. What is the integral of f(x) = 4x^3?
-
A.
x^4 + C
-
B.
x^4
-
C.
x^3 + C
-
D.
4x^4 + C
Solution
The integral ∫4x^3 dx = x^4 + C.
Correct Answer:
A
— x^4 + C
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Q. What is the integral of f(x) = cos(x)?
-
A.
sin(x) + C
-
B.
-sin(x) + C
-
C.
tan(x) + C
-
D.
sec(x) + C
Solution
The integral is sin(x) + C.
Correct Answer:
A
— sin(x) + C
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Q. What is the integral of sin(x) dx? (2021)
-
A.
-cos(x) + C
-
B.
cos(x) + C
-
C.
sin(x) + C
-
D.
-sin(x) + C
Solution
The integral of sin(x) is -cos(x) + C.
Correct Answer:
A
— -cos(x) + C
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Q. What is the integral of tan(x) dx? (2023)
-
A.
-ln
-
B.
cos(x)
-
C.
+ C
-
D.
ln
-
.
sin(x)
-
.
+ C
-
.
ln
-
.
tan(x)
-
.
+ C
-
.
-ln
-
.
sin(x)
-
.
+ C
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of tan(x) with respect to x? (2021)
-
A.
-ln
-
B.
cos(x)
-
C.
+ C
-
D.
ln
-
.
sin(x)
-
.
+ C
-
.
ln
-
.
tan(x)
-
.
+ C
-
.
-ln
-
.
sin(x)
-
.
+ C
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of tan(x)? (2021)
-
A.
-ln
-
B.
cos(x)
-
C.
+ C
-
D.
ln
-
.
sin(x)
-
.
+ C
-
.
ln
-
.
tan(x)
-
.
+ C
-
.
-ln
-
.
sin(x)
-
.
+ C
Solution
The integral of tan(x) is -ln|cos(x)| + C.
Correct Answer:
A
— -ln
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Q. What is the integral of the function f(x) = 3x^2? (2021)
-
A.
x^3 + C
-
B.
x^3 + 3C
-
C.
x^3 + 1
-
D.
3x^3 + C
Solution
The integral of 3x^2 is (3/3)x^3 + C = x^3 + C.
Correct Answer:
A
— x^3 + C
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Q. What is the integral of x^2 with respect to x? (2021)
-
A.
(1/3)x^3 + C
-
B.
(1/2)x^2 + C
-
C.
(1/4)x^4 + C
-
D.
(1/5)x^5 + C
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C. Here, n=2, so the integral is (1/3)x^3 + C.
Correct Answer:
A
— (1/3)x^3 + C
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Q. What is the integral of x^3 + 2x? (2021)
-
A.
(1/4)x^4 + x^2 + C
-
B.
(1/3)x^3 + x^2 + C
-
C.
(1/4)x^4 + (1/2)x^2 + C
-
D.
(1/5)x^5 + (1/2)x^2 + C
Solution
Integrating term by term, ∫x^3dx = (1/4)x^4 and ∫2xdx = x^2. Thus, ∫(x^3 + 2x)dx = (1/4)x^4 + (1/2)x^2 + C.
Correct Answer:
C
— (1/4)x^4 + (1/2)x^2 + C
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Q. What is the integral of x^n dx, where n ≠ -1? (2023)
-
A.
(x^(n+1))/(n+1) + C
-
B.
(x^(n-1))/(n-1) + C
-
C.
nx^(n-1) + C
-
D.
x^n + C
Solution
The integral of x^n dx is (x^(n+1))/(n+1) + C.
Correct Answer:
A
— (x^(n+1))/(n+1) + C
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Q. What is the integral of x^n where n ≠ -1? (2021)
-
A.
(1/n)x^(n+1) + C
-
B.
(1/(n+1))x^n + C
-
C.
(1/(n+1))x^(n+1) + C
-
D.
nx^(n-1) + C
Solution
The integral of x^n is (1/(n+1))x^(n+1) + C, provided n ≠ -1.
Correct Answer:
C
— (1/(n+1))x^(n+1) + C
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Q. What is the integrated rate law for a first-order reaction?
-
A.
ln[A] = -kt + ln[A]0
-
B.
[A] = [A]0 - kt
-
C.
[A] = [A]0e^(-kt)
-
D.
1/[A] = kt + 1/[A]0
Solution
The integrated rate law for a first-order reaction is ln[A] = -kt + ln[A]0.
Correct Answer:
A
— ln[A] = -kt + ln[A]0
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Q. What is the integrating factor for the equation dy/dx + (1/x)y = 2?
-
A.
x
-
B.
e^(ln(x))
-
C.
e^(ln(x^2))
-
D.
1/x
Solution
The integrating factor is e^(∫(1/x)dx) = e^(ln(x)) = x.
Correct Answer:
C
— e^(ln(x^2))
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Q. What is the integrating factor for the equation dy/dx + 2y = 3?
-
A.
e^(2x)
-
B.
e^(-2x)
-
C.
e^(3x)
-
D.
e^(-3x)
Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer:
A
— e^(2x)
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Q. What is the integrating factor for the equation dy/dx + 2y = 3x?
-
A.
e^(2x)
-
B.
e^(-2x)
-
C.
e^(3x)
-
D.
e^(-3x)
Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer:
A
— e^(2x)
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Q. What is the integrating factor for the equation dy/dx + 2y = 6?
-
A.
e^(2x)
-
B.
e^(-2x)
-
C.
e^(6x)
-
D.
e^(-6x)
Solution
The integrating factor is e^(∫2dx) = e^(2x).
Correct Answer:
A
— e^(2x)
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Q. What is the integrating factor for the equation dy/dx + 3y = 6?
-
A.
e^(3x)
-
B.
e^(-3x)
-
C.
3e^(3x)
-
D.
3e^(-3x)
Solution
The integrating factor is e^(∫3dx) = e^(3x).
Correct Answer:
A
— e^(3x)
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Q. What is the integrating factor for the equation dy/dx + 3y = 6x?
-
A.
e^(3x)
-
B.
e^(-3x)
-
C.
e^(6x)
-
D.
e^(-6x)
Solution
The integrating factor is e^(∫3dx) = e^(3x).
Correct Answer:
A
— e^(3x)
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Q. What is the interquartile range (IQR) of the data set {1, 3, 5, 7, 9, 11, 13, 15}?
Solution
Q1 = 4, Q3 = 10. IQR = Q3 - Q1 = 10 - 4 = 6.
Correct Answer:
B
— 6
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9, 10}?
Solution
IQR = Q3 - Q1; Q1 = 3, Q3 = 8; IQR = 8 - 3 = 5.
Correct Answer:
A
— 5
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Q. What is the interquartile range (IQR) of the data set {1, 3, 7, 8, 9}?
Solution
Q1 = 3, Q3 = 8. IQR = Q3 - Q1 = 8 - 3 = 5.
Correct Answer:
A
— 6
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Q. What is the interquartile range (IQR) of the data set: 1, 2, 3, 4, 5, 6, 7, 8, 9?
Solution
Q1 = 3, Q3 = 7; IQR = Q3 - Q1 = 7 - 3 = 4.
Correct Answer:
A
— 4
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Q. What is the interquartile range (IQR) of the data set: 1, 3, 5, 7, 9, 11, 13?
Solution
Q1 = 3, Q3 = 9. IQR = Q3 - Q1 = 9 - 3 = 6.
Correct Answer:
B
— 6
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