Aptarimas:Matematika/Dvilypiai integralai: Skirtumas tarp puslapio versijų

Ištrintas turinys Pridėtas turinys
225 eilutė:
:<math>z_{20}=x_{20}^2=4^2=16.</math>
 
: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 nepadaugintus iš <math>\pi<math>:
:<math>V_1a_1=\sqrt{r_1^2+(y_1-y_0)^2}=\sqrt{(0.2-0)^2+(0.04-0)^2}=\sqrt{0.2^2+0.04^2}=\sqrt{0.04+0.0016}=\sqrt{0.0416}=0.20396078;</math>
:<math>V_2a_2=\sqrt{r_2^2+(y_2-y_1)^2}=\sqrt{(0.4-0.2)^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>V_3a_3=\sqrt{r_3^2+(y_3-y_2)^2}=\sqrt{(0.6-0.4)^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>V_4a_4=\sqrt{r_4^2+(y_4-y_3)^2}=\sqrt{(0.8-0.6)^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>V_5a_5=\sqrt{r_5^2+(y_5-y_4)^2}=\sqrt{(1-0.8)^2+(1-0.64)^2}=\sqrt{0.2^2+0.36^2}=\sqrt{0.04+0.1296}=\sqrt{0.1696}=0.411825205;</math>
:<math>V_6a_6=\sqrt{r_6^2+(y_6-y_5)^2}=\sqrt{(1.2-1)^2+(1.44-1)^2}=\sqrt{0.2^2+0.44^2}=\sqrt{0.04+0.1936}=\sqrt{0.2336}=0.483321838;</math>
:<math>V_7a_7=\sqrt{r_7^2+(y_7-y_6)^2}=\sqrt{(1.4-1.2)^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>V_8a_8=\sqrt{r_8^2+(y_8-y_7)^2}=\sqrt{(1.6-1.4)^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>V_9a_9=\sqrt{r_9^2+(y_9-y_8)^2}=\sqrt{(1.8-1.6)^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>V_a_{10}=\sqrt{r_{10}^2+(y_{10}-y_9)^2}=\sqrt{(2-1.8)^2+(4-3.24)^2}=\sqrt{0.2^2+0.76^2}=\sqrt{0.04+0.5776}=\sqrt{0.6176}=0.785875308;</math>
:<math>V_a_{11}=\sqrt{r_{11}^2+(y_{11}-y_{10})^2}=\sqrt{(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>V_a_{12}=\sqrt{r_{12}^2+(y_{12}-y_{11})^2}=\sqrt{(2.4-2.2)^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>V_a_{13}=\sqrt{r_{13}^2+(y_{13}-y_{12})^2}=\sqrt{(2.6-2.4)^2+(6.76-5.76)^2}=\sqrt{0.2^2+1^2}=\sqrt{0.04+1}=\sqrt{1.04}=1.019803903;</math>
:<math>V_a_{14}=\sqrt{r_{14}^2+(y_{14}-y_{13})^2}=\sqrt{(2.8-2.6)^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>V_a_{15}=\sqrt{r_{15}^2+(y_{15}-y_{14})^2}=\sqrt{(3-2.8)^2+(9-7.84)^2}=\sqrt{0.2^2+1.16^2}=\sqrt{0.04+1.3456}=\sqrt{1.3856}=1.177115118;</math>
:<math>V_a_{16}=\sqrt{r_{16}^2+(y_{16}-y_{15})^2}=\sqrt{(3.2-3)^2+(10.24-9)^2}=\sqrt{0.2^2+1.24^2}=\sqrt{0.04+1.5376}=\sqrt{1.5776}=1.256025477;</math>
:<math>V_a_{17}=\sqrt{r_{17}^2+(y_{17}-y_{16})^2}=\sqrt{(3.4-3.2)^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>V_a_{18}=\sqrt{r_{18}^2+(y_{18}-y_{17})^2}=\sqrt{(3.6-3.4)^2+(12.96-11.56)^2}=\sqrt{0.2^2+1.4^2}=\sqrt{0.04+1.96}=\sqrt{2}=1.414213562;</math>
:<math>V_a_{19}=\sqrt{r_{19}^2+(y_{19}-y_{18})^2}=\sqrt{(3.8-3.6)^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>V_a_{20}=\sqrt{r_{20}^2+(y_{20}-y_{19})^2}=\sqrt{(4-3.8)^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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