Gryno formulė: Skirtumas tarp puslapio versijų

229 pridėti baitai ,  prieš 8 metus
:''Sprendimas''. Pasinaudodami [http://integrals.wolfram.com/index.jsp?expr=%28x%2Bx%5E2%29%5E2+*+%281%2B4*x%5E2%29%5E%281%2F2%29&random=false internetiniu integratoriumi], gauname:
:<math>m=\int_0^5 \gamma \sqrt{1+[y']^2} dx=\int_0^5 (x+y)^2\sqrt{1+[y']^2} dx=\int_0^5 (x+x^2)^2 \sqrt{1+4x^2} dx=</math>
:<math>=\frac{1}{7680}\left( 2\sqrt{4x^2+1} (640x^5+1536x^4+1000x^3+128x^2+105x-64)-105\text{arcsinh}(2x)\right)|_0^5=</math>
:<math>=\frac{1}{7680}\left( 2\sqrt{101} (640\cdot 3125+1536\cdot 625+1000\cdot 125+128\cdot 25+105\cdot 5-64)-105\text{arcsinh}(2\cdot 5)\right)-\frac{1}{7680}\left( 2\sqrt{1}\cdot (-64)-105\text{arcsinh}(0)\right)=</math>
 
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