$x sin x$ $xsinx$ is even or odd,?

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Answer 1 · 2018-05-10T08:53:13

Even

An even function is defined as one which:
$f (x) = f (- x)$ $f(x)=f(-x)$

An odd function is defined as one which:
$f (- x) = - f (x)$ $f(-x)=-f(x)$

We have $f (x) = x sin x$ $f(x)=xsinx$

$f (- x) = - x sin (- x)$ $f(-x)=-xsin(-x)$

Due to the nature of $sin x$ $sinx$ , $sin (- x) = - sin x$ $sin(-x)=-sinx$

So, $f (- x) = - x \cdot - sin x = x sin x = f (x)$ $f(-x)=-x*-sinx=xsinx=f(x)$

$f (x) = f (- x)$ $f(x)=f(-x)$

$x sin x$ $xsinx$ is therefore even,

xsinxxsinx is even or odd,?