Question

lf $f\left(x\right)$ is an even function, and $n\in N$, then ${\int }_{-\pi }^{\pi }f\left(x\right)\sin nxdx=$

• A. 0
• B. $2{\int }_0^{\pi }f\left(x\right)\sin nxdx$
• C. $4{\int }_0^{\frac{\pi }{2}}f\left(x\right)\sin nxdx$
• D. ${\int }_0^{\pi }f\left(x\right)\sin xdx$

Answer 1

The correct option is A 0

$f\left(x\right)$ even functions
$sinnx$ odd function
$t\left(x\right)sinnx$ is odd function
${\int }_{\pi }^{\pi }f\left(x\right)sinnxdx=0$