e-reader-frontend.macmillanlearning.com/?ro=macmillanlearning.com?rid=75ee9b80−04aa−4216−867e-e9e0b10f68e3?req_id=13f486c2−619b−429e... All Bookmarks 14. Find the area of the shaded region in Figure 18 enclosed by the circle r=21 and a petal of the curve r=cos3θ. Hint: Compute the area of both the petal and the region inside the petal and outside the circle. Rogawski et al., Calculus: Early Transcendentals, 4e, (C) 2019 W. H. Freeman and Company FIGURE 1815. Find the area of the inner loop of the lima\c{c}on with polar equation r=2cosθ−1 (Figure 19). 16. Find the area of the shaded region in Figure 19 between the inner and outer loop of the lima\c{c}on r=2cosθ−1.
Q. e-reader-frontend.macmillanlearning.com/?ro=macmillanlearning.com?rid=75ee9b80−04aa−4216−867e-e9e0b10f68e3?req_id=13f486c2−619b−429e... All Bookmarks 14. Find the area of the shaded region in Figure 18 enclosed by the circle r=21 and a petal of the curve r=cos3θ. Hint: Compute the area of both the petal and the region inside the petal and outside the circle. Rogawski et al., Calculus: Early Transcendentals, 4e, (C) 2019 W. H. Freeman and Company FIGURE 1815. Find the area of the inner loop of the lima\c{c}on with polar equation r=2cosθ−1 (Figure 19). 16. Find the area of the shaded region in Figure 19 between the inner and outer loop of the lima\c{c}on r=2cosθ−1.
Calculate Circle Area: Calculate the area of the circle with radius r=21.Area of a circle = πr2Calculation: π⋅(21)2=4π square units.
Calculate Petal Area: Calculate the area of one petal of the curve r=cos3θ.Area of one petal = 21∫(r2)dθ from 0 to 3π (since the petal repeats every 3π).Calculation: 21 * ∫(cos3θ)2dθ from 0 to 3π.Using the double angle identity, 210.Area = 21 * 212 from 0 to 3π = 215 square units.
Calculate Shaded Region Area: Calculate the area of the region inside the petal and outside the circle.Area of shaded region = Area of petal - Area of circle.Calculation: 12π−4π=−6π square units.
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