Question

intigration of 2sinxcosx​

Answer 1

☯ Explanation,

$\green \bigstar \tt \: \int 2 \sin(x) . \cos(x) \\ \\ \\ : \implies \tt \: \int 2 \sin(x).dx \\ \\ \\ : \implies {\underline {\boxed{\tt - \dfrac{1}{2} cos(2x) + c}}} \: \red \bigstar$

☯ Hence,

$\dag{ \boxed{ \tt{\int 2 \sin( x). \cos(x) = - \dfrac{1}{2} \cos(2x) + c }}}$

☯ Know to more,

• Power rule.

$\bull\tt \int x {}^{n} .dx \: \rightarrow \: \dfrac{x {}^{n + 1} }{n + 1} + c$

• Multiplication by constant (c).

$\bull\tt \int c \: f(x).dx \: \rightarrow \: c \int f(x).dx$

• Sum rule.

$\bull\tt \int (f + g)dx \rightarrow \: \int fdx \: + \: \int gdx$

• Difference rule.

$\bull \tt \int (f - g)dx \rightarrow \: \int fdx \: - \: \int gdx$