What is the integral from 0 to 2 of (1/2+y+z) ?

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

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

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

2 z + 3

Solution steps

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

Apply the Sum Rule:

\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

Simplify

= 2 z + 3

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\int_{1}^{2} x^{2} + \frac{1}{x ^{2}} d x

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\int_{1}^{2} 3 - x - \frac{2}{x} d x

What is the integral from 0 to 2 of (1/2+y+z) ?
The integral from 0 to 2 of (1/2+y+z) is 2z+3