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
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Find the area of the region that is inside both
equations.
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HW 61: 13.4 #3, 7, 11, 15, 19, 23 (Integrals in polar coordinates)Name_________________ Period: ___ Date:______
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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 +
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