Math Problem Statement
Use a double integral to find the area of the region bounded by all leaves of the rose
requals=sine 7 thetasin7θ.
Question content area bottom
Part 1
Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area the leaf that is closest to the positive x-axis.
Upper A Subscript leafAleafequals=Integral from 0 to StartFraction pi Over 7 EndFraction Integral from 0 to sine left parenthesis 7 theta right parenthesis r dr font size decreased by 5 d theta∫00StartFraction pi Over 7 EndFractionπ7∫00sine left parenthesis 7 theta right parenthesissin(7θ)r dr dθ
(Type exact answers, using
piπ
as needed.)
Part 2
Find the area of the region.
Upper A Subscript roseAroseequals=StartFraction 2 Over 21 EndFraction221
units squaredunits2
(Type an exact answer, using
piπ
as needed.)
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Polar Coordinates
Double Integration
Area Calculation
Formulas
Area in polar coordinates: A = ∫∫ r dr dθ
Equation of the rose curve: r = sin(7θ)
Theorems
Symmetry in Polar Curves
Integration in Polar Coordinates
Suitable Grade Level
Grades 11-12, College
Related Recommendation
Evaluate the Integral of the Four-Leaved Rose Curve in the First Quadrant
Finding the Area of a Petal in the Rose Curve r = cos(2θ)
Calculate the Area Enclosed by the Polar Rose Curve r = 6cos(5θ)
Find the Area of a Polar Curve Petal for r = 2 cos(2θ)
Area of Region in First Quadrant Defined by Polar Curve r = 6(3 - sin(2θ))^1/2