Page:Mémoires de l’Académie des sciences, Tome 5.djvu/416

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Des Valeurs numériques des Intégrales $\int dv.\cos qv^{2}$ et $\int dv.\sin qv^{2}.$

$\scriptstyle {\begin{array}{c|c|c|||c|c|c}{\text{LIMITES}}&&&{\text{LIMITES}}\\{\text{des intégrales}}.&\int dv.\cos qv^{2}.&\int dv.\sin qv^{2}.&{\text{des intégrales}}.&\int dv.\cos qv^{2}.&\int dv.\sin qv^{2}.\\\hline {\text{de }}v=0^{\mathrm {q} }&&{\text{de }}v=0^{\mathrm {q} }&&\\{\text{à }}v=0^{\mathrm {q} }{,}10.&0,0999.&0,0006.&{\text{à }}v=2^{\mathrm {q} },90.&0,5627.&0,4098.\\{\text{à}}v=0,20.&0,1999.&0,0042.&{\text{à }}3{,}00.&0,6061.&0,4959.\\0{,}30.&0{,}2993.&0{,}0140.&3{,}10.&0{,}5621.&0{,}5815.\\0{,}40.&0{,}3974.&0{,}0332.&3{,}20.&0{,}4668.&0{,}5931.\\0{,}50.&0{,}4923.&0{,}0644.&3{,}30.&0{,}4061.&0{,}5191.\\0{,}60.&0{,}5811.&0{,}1101.&3{,}40.&0{,}4388.&0{,}4294.\\0{,}70.&0{,}6597.&0{,}1716.&3{,}S0.&0{,}5328.&0{,}4149.\\0{,}80.&0{,}7230.&0{,}2487.&3{,}60.&0{,}5883.&0{,}4919.\\0{,}90.&0{,}7651.&0{,}3391.&3{,}70.&0{,}5424.&0{,}5746.\\1{,}00.&0{,}7803.&0{,}4376.&3{,}80.&0{,}4485.&0{,}5654.\\1{,}10.&0{,}7643.&0{,}5359.&3{,}90.&0{,}4226.&0{,}4750.\\1{,}20.&0{,}7161.&0{,}6229.&4{,}00.&0{,}4986.&0{,}4202.\\1{,}30.&0{,}6393.&0{,}6859.&4{,}10.&0{,}5739.&0{,}4754.\\1{,}40.&0{,}5439.&0{,}7132.&4{,}20.&0{,}5420.&0{,}5628.\\1{,}50.&0{,}4461.&0{,}6973.&4{,}30.&0{,}4497.&0{,}5537.\\1{,}60.&0{,}3662.&0{,}6388.&4{,}40.&0{,}4385.&0{,}4620.\\1{,}70.&0{,}3245.&0{,}5492.&4{,}50.&0{,}5261.&0{,}4339.\\1{,}80.&0{,}3342.&0{,}4509.&4{,}60.&0{,}5674.&0{,}5158.\\1{,}90.&0{,}3949.&0{,}3732.&4{,}70.&0{,}4917.&0{,}5668.\\2{,}00.&0{,}4886.&0{,}3432.&4{,}80.&0{,}4340.&0{,}4965.\\2{,}10.&0{,}5819.&0{,}3739.&4{,}90.&0{,}5003.&0{,}4347.\\2{,}20.&0{,}6367.&0{,}4553.&5{,}00.&0{,}5638.&0{,}4987.\\2{,}30.&0{,}6271.&0{,}5528.&5{,}10.&0{,}5000.&0{,}5620.\\2{,}40.&0{,}5556.&0{,}6194.&5{,}20.&0{,}4390.&0{,}4966.\\2{,}50.&0{,}4581.&0{,}6190.&5{,}30.&0{,}5078.&0{,}4401.\\2{,}60.&0{,}3895.&0{,}5499.&5{,}40.&0{,}5573.&0{,}5136.\\2{,}70.&0{,}3929.&0{,}4528.&5{,}50.&0{,}4785.&0{,}5533.\\2{,}80.&0{,}4678.&0{,}3913.\end{array}}$

$\int dv\cos qv^{2}$ et $\int dv\sin qv^{2}$ prises depuis zéro jusqu’à l’infini, sont égales l’une et l’autre à ${\frac {1}{2}}.$ Ainsi, pour avoir, à