What is the integral from 10 to 15 of ((y-10)/8) ?

The integral from 10 to 15 of ((y-10)/8) is 25/16

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integral from 10 to 15 of ((y-10)/8)

\int_{10}^{15} (\frac{y - 10}{8}) d y

\frac{25}{16}

Solution steps

\int_{10}^{15} \frac{y - 10}{8} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int_{10}^{15} y - 10 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

= \frac{1}{8} (\int_{10}^{15} y d y - \int_{10}^{15} 10 d y)

\int_{10}^{15} y d y = \frac{125}{2}

\int_{10}^{15} 10 d y = 50

= \frac{1}{8} (\frac{125}{2} - 50)

Simplify

\frac{1}{8} (\frac{125}{2} - 50) : \frac{25}{16}

= \frac{25}{16}

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What is the integral from 10 to 15 of ((y-10)/8) ?
The integral from 10 to 15 of ((y-10)/8) is 25/16