
Definite Integration: Substitution
Authored by Nidhi Mehta
Mathematics
12th Grade

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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the definite integral of 3x^2 * (x^3 + 2)^4 dx using the substitution method.
(1/5)(x^3 + 2)^4 + C
(1/4)(x^3 + 2)^5 + C
(1/6)(x^3 + 2)^5 + C
(1/5)(x^3 + 2)^5 + C
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Evaluate the definite integral of (2x + 1) / sqrt(x^2 + x + 1) dx using the substitution method.
2√(x^2 + x + 1) + C
4√(x^2 + x + 1) + C
√(x^2 + x + 1) + C
3√(x^2 + x + 1) + C
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Calculate the definite integral of sin(2x) * cos(2x) dx using the substitution method.
2sin(2x)cos(2x) + C
sin^2(4x) + C
cos^2(4x) + C
(1/4)sin^2(2x) + C
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Determine the value of the definite integral of x * sqrt(4 - x^2) dx using the substitution method.
(2/3)(4 - x^2)^(3/2) + C
(2/3)(4 - x^2)^(1/2) + C
(1/3)(4 - x^2)^(3/2) + C
(2/3)(4 - x^2)^(2/3) + C
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Find the definite integral of (x^2 + 1) / (x^3 + 3x) dx using the substitution method.
ln|x^3 + 3x| + C
ln|x^2 + 1| + C
ln|x^3 + 1| + C
ln|x^2 + 3x| + C
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Evaluate the definite integral of e^(2x) / (e^x + 1)^2 dx using the substitution method.
-1/(e^x + 1) + C
-1/(e^x + 1)^2 + C
-1/(e^x) + C
-1/(e^(2x) + 1) + C
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Calculate the definite integral of x * cos(x^2) dx using the substitution method.
cos(x^2) + C
(1/2) * sin(x^2) + C
x * cos(x^2)
x * sin(x^2) + C
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