Re: [考古] 97元智微積分考題(極座標)

看板trans_math作者LuisSantos ( )時間17年前 (2008/06/30 20:22)推噓1(1推 0噓 4→)

留言5則, 2人參與討論串2/6 (看更多)

※ 引述《hothero (hothero)》之銘言： : Find the length of r=1+sinθ : 請問這題心臟線的長度該如何求 : 煩請高手指點!! 所求弧長 π/2 = (2)(∫ √(r^2 + (dr/dθ)^2) dθ) -π/2 π/2 = (2)(∫ √((1+sinθ)^2 + (cosθ)^2) dθ) -π/2 π/2 = (2)(∫ √(2 + 2sinθ) dθ) -π/2 π/2 = (2)(√2)(∫ √(1+sinθ) dθ) -π/2 π/2 = (2)(√2)(∫ √(1 + (2)(sin(θ/2))(cos(θ/2))) dθ) -π/2 π/2 = (2)(√2)(∫ √((sin(θ/2) + cos(θ/2))^2) dθ) -π/2 π/2 = (2)(√2)(∫ |sin(θ/2) + cos(θ/2)| dθ) -π/2 π/2 = (2)(√2)(∫ sin(θ/2) + cos(θ/2) dθ) -π/2 |π/2 = (4)(√2)(-cos(θ/2) + sin(θ/2)) | |-π/2 π π -π -π = (4)(√2)((-cos(-) + sin(-)) - (-cos(---) + sin(---))) 4 4 4 4 π -π = (4)(√2)(sin(---) - sin(---)) 4 4 π π = (4)(√2)(sin(---) + sin(---)) 4 4 1 1 = (4)(√2)(---- + ----) √2 √2 = (4)(1 + 1) = (4)*(2) = 8 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.66.173.21

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hothero

06/30 20:35, , 1^F

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hothero

06/30 20:36, , 2^F

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hothero

06/30 20:37, , 3^F

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