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  • Prove the following (Exercises 34 to 39) Integral minus 1 to 1 x^17 cos^4 x dx

Prove the following (Exercises 34 to 39)

    Q36.    \int_{-1}^1x^{17}\cos^4 x dx=0

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Let \ x^{17}cos^{4}x=g(x)

g(-x)= (-x)^{17}cos^{4}(-x)=-x^{17}cos^{4}x=-g(x)

The Integrand g(x) therefore is an odd function and therefore 

\int_{-1}^{1}g(x)dx=0

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