What is the formula for integration by parts?

Integration Techniques and Trigonometric Identities

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Mathematics
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11th Grade - University
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Hard

Aiden Montgomery
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The integral of u dv is equal to u times v minus the integral of v du.
The integral of u dv is equal to v times u minus the integral of u dv.
The integral of u dv is equal to u times v plus the integral of v du.
The integral of u dv is equal to v times u plus the integral of u dv.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating the function x sin x dx using integration by parts?
x sine x minus cosine x plus c
Negative x cosine x plus sine x plus c
x cosine x minus sine x plus c
Negative x sine x plus cosine x plus c
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When using integration by parts, if u is chosen as ln x, what should dv be?
dv should be 1/x dx.
dv should be x dx.
dv should be dx.
dv should be ln x dx.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of ln x using integration by parts?
x ln x minus x plus c
ln x minus x plus c
ln x plus x plus c
x ln x plus x plus c
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which trigonometric identity is used to simplify the integral of cosine cubed x?
sine squared plus cosine squared equals one
tangent squared plus one equals secant squared
cosine squared equals one minus sine squared
sine squared equals one minus cosine squared
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the integration of cosine to the fifth power times sine to the fourth power, why is cosine split into two components?
To eliminate the sine function
To simplify the expression using u-substitution
To make the power even
To convert it into a sine function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of sine squared x using the half-angle identity?
One fourth x plus one half sine 2x plus c
One fourth x minus one half sine 2x plus c
One half x plus one fourth sine 2x plus c
One half x minus one fourth sine 2x plus c
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