
Understanding Indefinite Integrals with Trigonometric Substitution

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard

Emma Peterson
FREE Resource
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9 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main topic discussed in this video?
Calculating definite integrals
Finding the indefinite integral of 1 over 1 plus x squared
Solving differential equations
Finding the derivative of a function
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which substitution is used to simplify the integral?
x = sin(u)
x = cos(u)
x = tan(u)
x = sec(u)
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of tangent u with respect to u?
sin^2(u)
cos^2(u)
tan^2(u)
sec^2(u)
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which identity is used to simplify 1 plus tan squared u?
sin^2(u) + cos^2(u) = 1
1 + tan^2(u) = sec^2(u)
1 + sec^2(u) = tan^2(u)
tan^2(u) - sec^2(u) = 1
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integral of 1 with respect to u?
u + C
1/u + C
ln(u) + C
e^u + C
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What constant is added to the antiderivative?
F
C
D
E
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If x equals tangent u, what does u equal?
sin(x)
cos(x)
arctan(x)
sec(x)
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final expression for the indefinite integral of 1 over 1 plus x squared?
ln(x) + C
arctan(x) + C
e^x + C
x^2 + C
9.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What mathematical concept is primarily used in this video?
Partial fraction decomposition
Algebraic substitution
Trigonometric substitution
Logarithmic differentiation
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