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determinant-If-0-pi-2-4cos-2-4x-3-1-sin-2-2x-dx-a-2-b-Find-the-value-of-a-b-




Question Number 190186 by mnjuly1970 last updated on 29/Mar/23
       determinant (((         If  , Ω= ∫_0 ^( (π/2))  (( 4cos^( 2)  (4x))/(3(1+sin^( 2) (2x ))))dx= a(√2)  + b          )))                   ⇒  Find  the  value of   ,  a− b=?
$$ \\ $$$$\:\:\:\:\begin{array}{|c|}{\:\:\:\:\:\:\:\:\:\mathrm{If}\:\:,\:\Omega=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\:\mathrm{4cos}^{\:\mathrm{2}} \:\left(\mathrm{4}{x}\right)}{\mathrm{3}\left(\mathrm{1}+\mathrm{sin}^{\:\mathrm{2}} \left(\mathrm{2}{x}\:\right)\right)}\mathrm{d}{x}=\:{a}\sqrt{\mathrm{2}}\:\:+\:{b}\:\:\:\:\:\:\:\:\:\:}\\\hline\end{array}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\mathrm{Find}\:\:\mathrm{the}\:\:\mathrm{value}\:\mathrm{of}\:\:\:,\:\:{a}−\:{b}=? \\ $$$$ \\ $$
Commented by Frix last updated on 29/Mar/23
Ω=(−4+3(√2))π  a=3π∧b=−4π  a−b=7π
$$\Omega=\left(−\mathrm{4}+\mathrm{3}\sqrt{\mathrm{2}}\right)\pi \\ $$$${a}=\mathrm{3}\pi\wedge{b}=−\mathrm{4}\pi \\ $$$${a}−{b}=\mathrm{7}\pi \\ $$

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