
Understanding Polar Curves and Area Calculation

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

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the equation of the polar curve whose inner loop area we are trying to find?
r = 3 - 6 sin(θ)
r = 3 + 6 sin(θ)
r = 6 + 3 sin(θ)
r = 6 - 3 sin(θ)
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which formula is used to find the area bounded by a polar curve?
Area = integral of r dθ
Area = integral of r^2 dθ
Area = 1/2 integral of r^2 dθ
Area = 1/2 integral of r dθ
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the interval of integration for tracing the inner loop using the graphing calculator?
0 to 180 degrees
30 to 150 degrees
60 to 120 degrees
90 to 180 degrees
Tags
CCSS.HSF.TF.C.9
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can the interval of integration be determined analytically?
By setting r = 1
By setting r = 0
By setting θ = π
By setting θ = 0
Tags
CCSS.HSF.TF.C.9
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is used for simplifying the sine squared term in the integral?
1/2 (1 - sin(2θ))
1/2 (1 + cos(2θ))
1/2 (1 - cos(2θ))
1/2 (1 + sin(2θ))
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of 27/2 with respect to θ?
13.5 θ
27 θ
27/2 θ
54 θ
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate area of the inner loop calculated in the video?
5.8917 square units
3.8917 square units
2.8917 square units
4.8917 square units
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