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How do you find the antiderivative of #int (sin^7x)dx# from #[-1,1]#?

1 Answer

Jun 16, 2017

#int_-1^1sin^7xdx=0.#

Explanation:

We use the following Result to find the reqd. anti-derivative :

#int_a^af(x)dx=0,# if #f#is an odd continuous function on #[-a,a]. (a>0)#

The Proof of the Result is easy, so let us not bother about it.

# f(x)=sin^7x rArr f(-x)=sin^7(-x)=-sin^7x=-f(x).#

# :. f# is Odd.

Hence, by he Result, #int_(-1)^1sin^7xdx=0.#

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