Mathematics

Evaluate
$$\int _{ -1 }^{ 1 }{ { x }^{ 17 } } { cos }^{ 4 }xdx$$


SOLUTION
$$f(x)=x^{17}\cos^4 x$$
$$f(-x)=(-x)^{17}\cos^4 (-x)=x^{17}\cos^4 (x)=-f(x)$$
$$Hence$$ $$function$$ $$is$$ $$odd$$
$$By \space using \space the \space property \space of \space definite \space integral$$
$$\therefore \int_{-1}^{1}{x^{17}\cos^4 x.dx}=0$$
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Subjective Medium Published on 17th 09, 2020
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