Question

COROANĂ!
$\int\limits^ \frac{ \sqrt{3} }{4} _0 {arcsin (2x)} \, dx$

Answer 1

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Answer 2

rezolvi prin parti
u=arcsin2x;du=$\frac{2}{ \sqrt{1-x^2} }$
dv=dx;v=x
$\int\limits^ \frac{ \sqrt{3} }{2} _0 {arcsin2x} \, dx= xarcsin2x- \int\limits^ \frac{ \sqrt{3} }{2} _0 { \frac{2x}{ \sqrt{1-x^2} } } \, dx =xarcsinx+2 \ \sqrt{1-x^2} } = \\ = \frac{ \sqrt{3} }{2}* \frac{ \pi }{3}+2* \frac{1}{2}-0-2= \frac{ \sqrt{3 \pi } }{6}-1$