Question

${\int }_{-a}^a(si{n}^{6}x+si{n}^{7}x)dx$ is equal to

• A. $2{\int }_0^{a}si{n}^{6}xdx$
• B. $2{\int }_0^{a}si{n}^{7}xdx$
• C. $2{\int }_0^a(si{n}^{6}x+si{n}^{7}x)dx$
• D. zero

Answer 1

The correct option is A $2{\int }_0^{a}si{n}^{6}xdx$

$I={\int }_{-a}^{a}si{n}^{6}xdx+{\int }_{-a}^{a}si{n}^{7}xdx$
$\Rightarrow si{n}^{6}x$ is even function
$si{n}^{7}x$ is odd function
$I=2{\int }_0^{a}si{n}^{6}xdx+0$