Aptarimas:Matematika/Dvilypiai integralai: Skirtumas tarp puslapio versijų

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227 eilutė:
 
:Dabar sudėsime 20 diskų, kai kiekvieno disko aukštis yra <math>h_1=z_1-z_0</math>, <math>h_2=z_2-z_1</math>, <math>h_3=z_3-z_2</math> ir taip toliau. Gauname visų diskų tūrius padalintus iš <math>\pi</math>:
:<math>a_1=r_1^2(z_1-z_0)^2=0.2^2(0.04-0)^2=0.2^2\cdot 0.04^2=0.04\cdot 0.0016=0.000064;</math>
:<math>a_2=r_2^2(z_2-z_1)^2=0.4^2(0.16-0.04)^2=0.4^2\cdot 0.12^2=0.16\cdot 0.0144=0.002304;</math>
:<math>a_3=r_3^2(z_3-z_2)^2=0.6^2(0.36-0.16)^2=0.6^2\cdot 0.2^2=0.36\cdot 0.04=0.0144;</math>
:<math>a_4=r_4^2(z_4-z_3)^2=0.8^2(0.64-0.36)^2=0.8^2\cdot 0.28^2=0.64\cdot 0.0784=0.050176;</math>
:<math>a_5=r_5^2(z_5-z_4)^2=1^2(1-0.64)^2=1^2\cdot 0.36^2=1\cdot 0.1296=0.1296;</math>
:<math>a_6=r_6^2(z_6-z_5)^2=1.2^2(1.44-1)^2=1.2^2\cdot 0.44^2=1.44\cdot 0.1936=0.278784;</math>
:<math>a_7=r_7^2(z_7-z_6)^2=1.4^2(1.96-1.44)^2=1.4^2\cdot 0.52^2=1.96\cdot 0.2704=0.529984;</math>
:<math>a_8=r_8^2(z_8-z_7)^2=1.6^2(2.56-1.96)^2=1.6^2\cdot 0.6^2=2.56\cdot 0.36=0.9216;</math>
:<math>a_9=r_9^2(z_9-z_8)^2=1.8^2(3.24-2.56)^2=1.8^2\cdot 0.68^2=3.24\cdot 0.4624=1.498176;</math>
:<math>a_{10}=r_{10}^2(z_{10}-z_9)^2=2^2(4-3.24)^2=2^2\cdot 0.76^2=4\cdot 0.5776=2.3104;</math>
:<math>a_{11}=r_{11}^2(z_{11}-z_{10})^2=2.2^2(4.84-4)^2=2.2^2\cdot 0.84^2=4.84\cdot 0.7056=3.415104;</math>
:<math>a_{12}=r_{12}^2(z_{12}-z_{11})^2=2.4^2(5.76-4.84)^2=2.4^2\cdot 0.92^2=5.76\cdot 0.8464=4.875264;</math>
:<math>a_{13}=r_{13}^2(z_{13}-z_{12})^2=2.6^2(6.76-5.76)^2=2.6^2\cdot 1^2=6.76\cdot 1=6.76;</math>
:<math>a_{14}=r_{14}^2(z_{14}-z_{13})^2=2.8^2(7.84-6.76)^2=2.8^2\cdot 1.08^2=7.84\cdot 1.1664=9.144576;</math>
:<math>a_{15}=r_{15}^2(z_{15}-z_{14})^2=3^2(9-7.84)^2=3^2\cdot 1.16^2=9\cdot 1.3456=12.1104;</math>
:<math>a_{16}=r_{16}^2(z_{16}-z_{15})^2=3.2^2(10.24-9)^2=3.2^2\cdot 1.24^2=10.24\cdot 1.5376=15.745024;</math>
:<math>a_{17}=r_{17}^2(z_{17}-z_{16})^2=3.4^2(11.56-10.24)^2=3.4^2\cdot 1.32^2=11.56\cdot 1.7424=20.142144;</math>
:<math>a_{18}=r_{18}^2(z_{18}-z_{17})^2=3.6^2(12.96-11.56)^2=3.6^2\cdot 1.4^2=12.96\cdot 1.96=25.4016;</math>
:<math>a_{19}=r_{19}^2(z_{19}-z_{18})^2=3.8^2(14.44-12.96)^2=3.8^2\cdot 1.48^2=14.44\cdot 2.1904=31.629376;</math>
:<math>a_{20}=r_{20}^2(z_{20}-z_{19})^2=4^2(16-14.44)^2=4^2\cdot 1.56^2=16\cdot 2.4336=38.9376.</math>
 
 
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