Menu Close

# I-0-c-2-sin-2-d-tan-a-2-b-2-a-2-gt-b-2-c-2-gt-1-Perimeter-of-ellipse-4-0-pi-2-a-2-a-2-b-2-sin-2-d-is-that-right-sir-

Question Number 142708 by ajfour last updated on 05/Jun/21
$$\:{I}=\int_{\mathrm{0}} ^{\:\:\alpha} \sqrt{{c}^{\mathrm{2}} −\mathrm{sin}\:^{\mathrm{2}} \theta}{d}\theta \\$$$$\:\mathrm{tan}\:\alpha=\frac{{a}^{\mathrm{2}} }{{b}^{\mathrm{2}} }\:\:,\:{a}^{\mathrm{2}} >{b}^{\mathrm{2}} \:\:,\:{c}^{\mathrm{2}} >\mathrm{1} \\$$$${Perimeter}\:{of}\:{ellipse} \\$$$$=\mathrm{4}\int_{\mathrm{0}} ^{\:\:\pi/\mathrm{2}} \sqrt{{a}^{\mathrm{2}} −\left({a}^{\mathrm{2}} −{b}^{\mathrm{2}} \right)\mathrm{sin}\:^{\mathrm{2}} \theta}\:{d}\theta \\$$$$\left({is}\:{that}\:{right}\:{sir}?\right) \\$$
Answered by MJS_new last updated on 04/Jun/21
$$\int\sqrt{{c}^{\mathrm{2}} −\mathrm{sin}^{\mathrm{2}} \:\theta}\:{d}\theta={c}\int\sqrt{\mathrm{1}−{c}^{−\mathrm{2}} \mathrm{sin}^{\mathrm{2}} \:\theta}\:{d}\theta= \\$$$$={c}\mathrm{E}\:\left(\theta\mid{c}^{−\mathrm{2}} \right)\:+{C} \\$$
Commented by ajfour last updated on 05/Jun/21
$${whats}\:{the}\:{name}? \\$$
Commented by MJS_new last updated on 05/Jun/21
$$\mathrm{Incomplete}\:\mathrm{Elliptic}\:\mathrm{Integral}\:\mathrm{of}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{Kind} \\$$
Commented by mohammad17 last updated on 05/Jun/21
$${sir}\:{can}\:{you}\:{give}\:{me}\:{the}\:{formola} \\$$