Mathematics

If $$\displaystyle f(x)=\frac{{x}^{7}-3{x}^{5}+7{x}^{3}-x+1}{{\cos}^{2}x}$$ then $$\displaystyle \int_{-\pi/4}^{\pi/4}{f(x)}dx$$ is equals to 


ANSWER

$$2$$


SOLUTION
$$f\left( x \right) =\dfrac { { x }^{ 7 }-{ 3x }^{ 5 }+{ 7x }^{ 3 }-x+1 }{ { \cos }^{ 2 }x } $$
$$\int _{ \dfrac { -\pi  }{ 4 }  }^{ \dfrac { \pi  }{ 4 }  }{ f\left( x \right)  } dx\quad \quad \left\{ \because \quad f\left( x \right) =-f\left( -x \right)  \right\} $$
$$=\int _{ \dfrac { -\pi  }{ 4 }  }^{ \dfrac { \pi  }{ 4 }  }{ \dfrac { dx }{ { \cos }^{ 2 }x }  } $$
$$={ \left( tanx \right)  }_{ -\pi /4 }^{ \pi /4 }=2$$
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Single Correct Hard Published on 17th 09, 2020
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