What is the formula used to find the area enclosed by one petal of a polar curve?

Polar Curves and Area Calculations

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Mathematics
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10th - 12th Grade
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Hard

Emma Peterson
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The definite integral from alpha to beta of 1/2 r² dθ
The definite integral from alpha to beta of r² dθ
The definite integral from alpha to beta of 1/3 r² dθ
The definite integral from alpha to beta of r dθ
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many petals does the polar curve r = 2cos(3θ) have?
Four
Five
Three
Two
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the number in front of θ in the equation r = 2cos(3θ)?
It determines the color of the petals
It determines the length of the petals
It determines the number of petals
It determines the width of the petals
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
For the polar curve r² = 4cos(2θ), what is the total area enclosed by the curve?
2
4
6
8
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What method is used to find the angles that define the inner loop of the polar curve r = 1 + 2sin(θ)?
Setting r equal to 1
Setting r equal to 2
Setting r equal to 0
Setting r equal to -1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the area of the inner loop of r = 1 + 2sin(θ)?
Set r equal to zero
Calculate the integral
Graph the curve
Find the derivative
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When finding the entire area enclosed by r = 5 + 2sin(θ), over what interval should you integrate?
0 to π
0 to 4π
0 to 2π
0 to 3π
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