Check Out Parity

Calculus Level 3

For any real valued function f : [ − a , a ] → ℜ f: [-a,a] \to \Re ∀ a > 0 \forall a>0 we have the relation: ∫ − a a f ( x ) 2 d x = 2 ∫ 0 a f ( x ) 2 d x \displaystyle \int_{-a}^{a} {f(x)}^2dx=2\displaystyle \int_{0}^{a}{f(x)}^2dx Is this True of False? This is part of this set

True False

Hjalmar Orellana Soto by Hjalmar Orellana Soto , 24, Chile

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1 solution

This is only True for even and odd functions, but for any other function is False, for example f ( x ) = e x f(x)=e^x

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