Question

INTEGRAL

$integral \: \csc(5t) \cos(10t)$
de 0 até pi/2

Answer 1

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$\sf{cos(10t)=cos(2\cdot5t)=1-2sen^2(5t)}\\\displaystyle\sf{\int_{0}^{\frac{\pi}{2}}csc(5t)\cdot cos(10t)=\int_{0}^{\frac{\pi}{2}}}\dfrac{1-2sen^2(5t)}{sen(5t)~dt}\\\displaystyle\sf{\int_{0}^{\frac{\pi}{2}}csc(5t)~dt-2\int_{0}^{\frac{\pi}{2}}\dfrac{\diagdown\!\!\!\!\!\!sen^2(5t)}{\diagdown\!\!\!\!\!sen(5t)}~dt}}\\\displaystyle\sf{\dfrac{1}{5}\int_{0}^{\frac{\pi}{2}}5csc(5t)~dt-2\int_{0}^{\frac{\pi}{2}}sen(5t)~dt}$

$\displaystyle\sf{\dfrac{1}{5}\int_{0}^{\frac{\pi}{2}}5csc(5t)~dt}\not\exists}\\\sf{portanto~\int_{0}^{\frac{\pi}{2}}csc(5t)\cdot cos(10t)~dt\not\exists}$