Determine the value of the line integral ∫CF⋅dr\int_C \mathbf{F} \cdot d\mathbf{r}∫CF⋅dr for F=⟨yzcos(x),zsin(x),ysin(x)⟩\mathbf{F} = \langle yz \cos(x), z \sin(x), y \sin(x) \rangleF=⟨yzcos(x),zsin(x),ysin(x)⟩ along the path r(t)=⟨t2,ln(1+t),et⟩\mathbf{r}(t) = \langle t^2, \ln(1+t), e^t \rangler(t)=⟨t2,ln(1+t),et⟩ from t=0t=0t=0 to t=1t=1t=1.
esin(1)ln(2)e \sin(1) \ln(2)esin(1)ln(2)
sin(1)ln(2)+e\sin(1) \ln(2) + esin(1)ln(2)+e
sin(1)ln(2)\sin(1) \ln(2)sin(1)ln(2)
sin(1)ln(2)e\sin(1) \ln(2) esin(1)ln(2)e