求定积分$\int_{-\frac{\pi}{3}}^{\frac{\pi}{3}}\sin(x + \dfrac{\pi}{3})dx$.

求曲线$y = e^{-x}-\dfrac{1}{2}x^{2}$的凹凸区间.

求在区间$[0,\pi]$上曲线$y = \sin x$与$x$轴所围平面图形绕$x$轴旋转一周所得旋转体的体积.