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  • By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19. 13

By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.

    Q13.    \int_\frac{-\pi}{2}^\frac{\pi}{2}\sin^7xdx

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We have                          I\ =\ \int_\frac{-\pi}{2}^\frac{\pi}{2}\sin^7xdx

We know that      \sin^7x is  an odd function. 

So the following property holds here:-   

                                \int_{-a}^{a}f(x)dx\ =\ 0

Hence           

                                      I\ =\ \int_\frac{-\pi}{2}^\frac{\pi}{2}\sin^7xdx\ =\ 0

Posted by

Devendra Khairwa

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