HW 61: 13.4 #3, 7, 11, 15, 19, 23 (Integrals in polar coordinates)Name_________________ Period: ___ Date:______ #3 Find the area of the region bounded by the graph #7 of the polar equation. r = 1 − cosθ #11 Find the area of the region bounded by one loop of the graph of the polar equation. r = 3cos5θ Find the area of region R. R {(r ,θ ) : 0 ≤ θ ≤ = π 2 ,0 ≤ r ≤ eθ } #15 Set up integrals in polar coordinates that can be used to find the area of the region shown in the figure. HW 61: 13.4 #3, 7, 11, 15, 19, 23 (Integrals in polar coordinates)Name_________________ Period: ___ Date:______ #19 Find the area of the region that is outside the graph of the first equation #23 and inside the graph of the second equation. r = sin θ r = 3 cos θ r= 2 + 2cos θ r =3 # Find the area of the region that is inside both equations. # HW 61: 13.4 #3, 7, 11, 15, 19, 23 (Integrals in polar coordinates)Name_________________ Period: ___ Date:______ # # Answers 3π 3. 2 1 7. (eπ − 1) ≈ 5.54 4 9π 11. 20 arctan 3 1 (4 csc θ ) 2 − (2) 2 dθ 15. ∫ π /4 2 9 3 ≈ 14.08 2 5π 1 23. 3 ≈ 0.22 − 24 4 19. 2π + # #