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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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