integral from-1/2 to 0 of (1/2+2y+3z)

解

\int_{- \frac{1}{2}}^{0} (\frac{1}{2} + 2 y + 3 z) d y

\frac{3 z}{2}

解答ステップ

\int_{- \frac{1}{2}}^{0} \frac{1}{2} + 2 y + 3 z d y

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- \frac{1}{2}}^{0} \frac{1}{2} d y + \int_{- \frac{1}{2}}^{0} 2 y d y + \int_{- \frac{1}{2}}^{0} 3 z d y

\int_{- \frac{1}{2}}^{0} \frac{1}{2} d y = \frac{1}{4}

\int_{- \frac{1}{2}}^{0} 2 y d y = - \frac{1}{4}

\int_{- \frac{1}{2}}^{0} 3 z d y = \frac{3 z}{2}

= \frac{1}{4} - \frac{1}{4} + \frac{3 z}{2}

簡素化

= \frac{3 z}{2}