Question

Найдите площадь заштрихованной фигуры

Answer 1

1.  ∫x²/2-x+1 dx   [-2;4]  F(x)=x³/6-x²/2+x
     F(4)=10 2/3-8+4=4 2/3    F(-2)=-2 2/3-2-2=-6 2/3
      F(4)-F(-2)=4 2/3+6 2/3=11 1/3=S

2.   y=2sin2x   ∫2sin2xdx=2∫sin2xdx=-cos2x   [0;5π/12]
F(0)=-1   F(5π/12)=-cos(10π/12)=-cos(5π/6)=√3/2
F(5π/12)-F(0)=√3/2+1
s1=1/2*5π/12*12/5π*5π/12=5π/24
S=√3/2+1-5π/24