let-I-0-pi-xdx-cos-2-x-2-sin-2-x-with-real-1-find-the-value-of-I-2-calculate-0-pi-xdx-a-2-cos-2-x-b-2-sin-2-x-with-a-and-b-reals-

Tinku Tara June 4, 2023 Integration 0 Comments

Question Number 53285 by maxmathsup by imad last updated on 20/Jan/19

let I_λ =∫_0 ^π ((xdx)/(cos^2 x +λ^2 sin^2 x)) with λ real 1) find the value of I_λ 2) calculate ∫_0 ^π ((xdx)/(a^2 cos^2 x +b^2 sin^2 x)) with a and b reals.

$${let}\:{I}_{\lambda} \:=\int_{\mathrm{0}} ^{\pi} \:\:\:\frac{{xdx}}{{cos}^{\mathrm{2}} {x}\:+\lambda^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}\:\:{with}\:\lambda\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{I}_{\lambda} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{xdx}}{{a}^{\mathrm{2}} {cos}^{\mathrm{2}} {x}\:+{b}^{\mathrm{2}} {sin}^{\mathrm{2}} {x}}\:{with}\:{a}\:{and}\:{b}\:{reals}. \\ $$

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