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휋/3 
3 cos휃 
= 
−휋/3 1+cos휃 
A =∬ 푟푑푟 푑휃 = 푅 ∫ ∫ 푟푑푟 푑휃 
휋/3 
−휋/3 
2/2 | 3 cos휃 
∫ 푟 
1+cos휃 d휃 
= ∫ 
(3cos휃) 
2 
휋 
3 
−휋 
3 
2 
- 
(1+cos휃)2 
2 
d휃 
= ∫ 
8푐표푠휃2−1−2 cos휃 
2 
휋 
3 
−휋 
3 
d휃 
1 
2 
= 
휋 
3 
−휋 
3 
휋 
3 
−휋 
3 
휋 
3 
−휋 
3 
(∫ 8 cos 휃2 푑휃 − ∫ 1 푑휃 − ∫ 2 cos 휃 푑휃 
) = 
= 
1 
2 
(4 ( 휃 + 
1 
2 
sin 2휃 )| 휋 /3 
휋 
3 
−휋/3) −( 
+ 
휋 
3 
) - ( 
2√3 
2 
+ 
2√3 
2 
) 
= 
4휋 
3 
-√3

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Question 2 c Math 1

  • 1. 휋/3 3 cos휃 = −휋/3 1+cos휃 A =∬ 푟푑푟 푑휃 = 푅 ∫ ∫ 푟푑푟 푑휃 휋/3 −휋/3 2/2 | 3 cos휃 ∫ 푟 1+cos휃 d휃 = ∫ (3cos휃) 2 휋 3 −휋 3 2 - (1+cos휃)2 2 d휃 = ∫ 8푐표푠휃2−1−2 cos휃 2 휋 3 −휋 3 d휃 1 2 = 휋 3 −휋 3 휋 3 −휋 3 휋 3 −휋 3 (∫ 8 cos 휃2 푑휃 − ∫ 1 푑휃 − ∫ 2 cos 휃 푑휃 ) = = 1 2 (4 ( 휃 + 1 2 sin 2휃 )| 휋 /3 휋 3 −휋/3) −( + 휋 3 ) - ( 2√3 2 + 2√3 2 ) = 4휋 3 -√3