Aptarimas:Matematika/Dvilypiai integralai: Skirtumas tarp puslapio versijų

Ištrintas turinys Pridėtas turinys
226 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(y_1-y_0)^2=0.2^2+(0.04-0)^2=\sqrt{0.2^2+0.04^2}=\sqrt{0.04+0.0016}=\sqrt{0.0416}=0.20396078;</math>
:<math>a_2=r_2^2(y_2-y_1)^2=0.4^2+(0.16-0.04)^2=\sqrt{0.2^2+0.12^2}=\sqrt{0.04+0.0144}=\sqrt{0.0544}=0.233238075;</math>
:<math>a_3=r_3^2(y_3-y_2)^2=0.6^2+(0.36-0.16)^2=\sqrt{0.2^2+0.2^2}=\sqrt{0.04+0.04}=\sqrt{0.08}=0.282842712;</math>
:<math>a_4=r_4^2(y_4-y_3)^2=0.8^2+(0.64-0.36)^2=\sqrt{0.2^2+0.28^2}=\sqrt{0.04+0.0784}=\sqrt{0.1184}=0.34409301;</math>
:<math>a_5=r_5^2(y_5-y_4)^2=1^2+(1-0.64)^2=\sqrt{0.2^2+0.36^2}=\sqrt{0.04+0.1296}=\sqrt{0.1696}=0.411825205;</math>
:<math>a_6=r_6^2(y_6-y_5)^2=1.2^2+(1.44-1)^2=\sqrt{0.2^2+0.44^2}=\sqrt{0.04+0.1936}=\sqrt{0.2336}=0.483321838;</math>
:<math>a_7=r_7^2(y_7-y_6)^2=1.4^2+(1.96-1.44)^2=\sqrt{0.2^2+0.52^2}=\sqrt{0.04+0.2704}=\sqrt{0.3104}=0.557135531;</math>
:<math>a_8=r_8^2(y_8-y_7)^2=1.6^2+(2.56-1.96)^2=\sqrt{0.2^2+0.6^2}=\sqrt{0.04+0.36}=\sqrt{0.4}=0.632455532;</math>
:<math>a_9=r_9^2(y_9-y_8)^2=1.8^2+(3.24-2.56)^2=\sqrt{0.2^2+0.68^2}=\sqrt{0.04+0.4624}=\sqrt{0.5024}=0.708801805;</math>
:<math>a_{10}=r_{10}^2(y_{10}-y_9)^2=2^2+(4-3.24)^2=\sqrt{0.2^2+0.76^2}=\sqrt{0.04+0.5776}=\sqrt{0.6176}=0.785875308;</math>
:<math>a_{11}=r_{11}^2(y_{11}-y_{10})^2=2.2^2+(4.84-4)^2=\sqrt{0.2^2+0.84^2}=\sqrt{0.04+0.7056}=\sqrt{0.7456}=0.863481325;</math>
:<math>a_{12}=r_{12}^2(y_{12}-y_{11})^2=2.4^2+(5.76-4.84)^2=\sqrt{0.2^2+0.92^2}=\sqrt{0.04+0.8464}=\sqrt{0.8864}=0.941488183;</math>
:<math>a_{13}=r_{13}^2(y_{13}-y_{12})^2=2.6^2+(6.76-5.76)^2=\sqrt{0.2^2+1^2}=\sqrt{0.04+1}=\sqrt{1.04}=1.019803903;</math>
:<math>a_{14}=r_{14}^2(y_{14}-y_{13})^2=2.8^2+(7.84-6.76)^2=\sqrt{0.2^2+1.08^2}=\sqrt{0.04+1.1664}=\sqrt{1.2064}=1.098362417;</math>
:<math>a_{15}=r_{15}^2(y_{15}-y_{14})^2=3^2+(9-7.84)^2=\sqrt{0.2^2+1.16^2}=\sqrt{0.04+1.3456}=\sqrt{1.3856}=1.177115118;</math>
:<math>a_{16}=r_{16}^2(y_{16}-y_{15})^2=3.2^2+(10.24-9)^2=\sqrt{0.2^2+1.24^2}=\sqrt{0.04+1.5376}=\sqrt{1.5776}=1.256025477;</math>
:<math>a_{17}=r_{17}^2(y_{17}-y_{16})^2=3.4^2+(11.56-10.24)^2=\sqrt{0.2^2+1.32^2}=\sqrt{0.04+1.7424}=\sqrt{1.7824}=1.335065541;</math>
:<math>a_{18}=r_{18}^2(y_{18}-y_{17})^2=3.6^2+(12.96-11.56)^2=\sqrt{0.2^2+1.4^2}=\sqrt{0.04+1.96}=\sqrt{2}=1.414213562;</math>
:<math>a_{19}=r_{19}^2(y_{19}-y_{18})^2=3.8^2+(14.44-12.96)^2=\sqrt{0.2^2+1.48^2}=\sqrt{0.04+2.1904}=\sqrt{2.2304}=1.493452376;</math>
:<math>a_{20}=r_{20}^2(y_{20}-y_{19})^2=4^2+(16-14.44)^2=\sqrt{0.2^2+1.56^2}=\sqrt{0.04+2.4336}=\sqrt{2.4736}=1.57276826.</math>
 
 
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