→ iyenn: 學長好棒~~:) 01/20 10:13
推 abcxyz123:謝謝學長~啾咪^.^ 01/20 12:58
※ 引述《abcxyz123 (阿里八八與四十大盜)》之銘言：
: Calculate the area of the region bounded by the circle C:x^2+y^2=9x+16y
: 這題的前一小題是有證出area of D =0.5∫(-ydx+xdy) so 可能會用到
: 答案:337π/4
公式可以的，前提你會參數化就好
圓心偏移的參數化
x = r cost + a
y = r sint + b
r = √337/4
a = √81/4 = 9/2
b = √64 = 8
D =0.5∫(-ydx+xdy)
= 0.5 ∮ -(r sint + b) (-r sint dt ) + ( rcost + a) (r cost dt)
c
2π 2 2 2 2
= 0.5 ∫ r sin t dt + b r sint dt + r cos t dt + a r cost dt
0
2π 2
= 0.5 ∫ r + b r sint + a r cost dt
0
2
= 0.5 * 2π * r
2
= r π = 337/4 π
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