Question

интеграл от π/12 до π/9 (dx/sin²3x)

Answer 1

$\int\limits^ \frac{ \pi }{9} _\frac{ \pi }{12}{ \frac{1}{sin^2(3x)} } \, dx\\F(x)= -\frac{1}{3}*ctg(3x)\\\int\limits^ \frac{ \pi }{9} _\frac{ \pi }{12}{ \frac{1}{sin^2(3x)} } \, dx= -\frac{1}{3}*ctg(3* \frac{ \pi }{9} ) - (-\frac{1}{3}*ctg(3* \frac{ \pi }{12} ))=\\= -\frac{1}{3}*\frac{ \sqrt{3} }{3}-(- \frac{1}{3}* 1)= -\frac{ \sqrt{3} }{9}+\frac{1}{3}$