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

解答

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

2 z + 3

求解步骤

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

使用积分加法定则:

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

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

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

\int_{0}^{2} z d y = 2 z

\int_{0}^{2} y d y = 2

= 1 + 2 z + 2

化简

= 2 z + 3

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