Question

sin2*x-cos*3x+1 решить определенный интеграл (1;-1)

Answer 1

[-1;1] ∫ (sin2x-cos3x+1) dx = 
= [-1;1]  (-1/2 cos2x - 1/3 sin3x +x)  = 
= -1/2 ( cos (2*1) - cos(2*(-1) ) - 1/3 ( sin(3*1) - sin(3*(-1) )  + 1 -(-1)  =
= -1/2 ( cos (2) - cos(-2) ) - 1/3 ( sin(3) - sin(-3) )  + 2  =
= -1/2 ( cos (2) - cos(2) ) - 1/3 ( sin(3) + sin(3) )  + 2  =
= -1/2 * 0 - 1/3 * 2sin(3) + 2  =
=  2/3 * (  3 - sin(3)  )