L=∫141+((y4/8+1/(4y2))′)2dy=∫141+(y3/2−1/(2y3))2dy=∫141+(y6/4−1/2+1/(4y6)dy=∫141+y6/4−1/2+1/(4y6)dy=∫14y6/4+1/2+1/(4y6)dy=∫14(y3/2+1/(2y3)2dy=∫14(y3/2+1/(2y3))dy=(y4/8−y−2)∣14=(44/8−4−2)−(14/8−1−2)==32−1/16−1/8+1=33−3/16=525/16L=∫_1^4 \sqrt{1+((y^4/8+1/(4y^2))')^2}dy =∫_1^4 \sqrt{1+(y^3/2-1/(2y^3))^2}dy=∫_1^4 \sqrt{1+(y^6/4-1/2+1/(4y^6)}dy=\\∫_1^4 \sqrt{1+y^6/4-1/2+1/(4y^6)}dy=∫_1^4 \sqrt{y^6/4+1/2+1/(4y^6)}dy=∫_1^4 \sqrt{(y^3/2+1/(2y^3)^2}dy=\\∫_1^4 (y^3/2+1/(2y^3))dy= (y^4/8-y^{-2})|_1^4=(4^4/8-4^{-2})-(1^4/8-1^{-2})=\\=32-1/16-1/8+1=33-3/16=525/16L=∫141+((y4/8+1/(4y2))′)2dy=∫141+(y3/2−1/(2y3))2dy=∫141+(y6/4−1/2+1/(4y6)dy=∫141+y6/4−1/2+1/(4y6)dy=∫14y6/4+1/2+1/(4y6)dy=∫14(y3/2+1/(2y3)2dy=∫14(y3/2+1/(2y3))dy=(y4/8−y−2)∣14=(44/8−4−2)−(14/8−1−2)==32−1/16−1/8+1=33−3/16=525/16
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