
Evaluating Definite Integrals and Logarithms

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial problem statement discussed in the video?
Differentiating cos(2x) over 1 + sin(2x)
Integrating cos(2x) over 1 + sin(2x)
Differentiating sin(2x) over 1 + cos(2x)
Integrating sin(2x) over 1 + cos(2x)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can't the given integral be split into two separate fractions?
Because it is already simplified
Because it involves trigonometric functions
Because the sum is in the numerator
Because the sum is in the denominator
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is used to simplify the integral?
U = 1 + cos(2x)
U = cos(2x)
U = sin(2x)
U = 1 + sin(2x)
Tags
CCSS.HSF.TF.C.9
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which formula is ultimately used to solve the integral after substitution?
Basic trigonometric integral formula
Logarithmic formula
Polynomial formula
Exponential formula
Tags
CCSS.HSF.TF.C.9
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What identity is used in the new example involving a definite integral?
tan(2x) - 1 = sec(2x)
sec(2x) + 1 = tan(2x)
tan(2x) + 1 = sec(2x)
sec(2x) - 1 = tan(2x)
Tags
CCSS.HSF.TF.C.9
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of evaluating the definite integral from pi/4 to 0?
Positive natural log of sqrt(2)/2
Negative natural log of sqrt(2)/2
One
Zero
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can the final answer be expressed using logarithmic properties?
As a product of two natural logs
As a sum of two natural logs
As a difference of two natural logs
As a single natural log
Tags
CCSS.HSF.TF.A.2
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