What is the integral from-7 to 0 of (y/7+sqrt(y+8)) ?

The integral from-7 to 0 of (y/7+sqrt(y+8)) is -7/2+(32sqrt(2)-2)/3

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integral from-7 to 0 of (y/7+sqrt(y+8))

\int_{- 7}^{0} (\frac{y}{7} + y + 8) d y

- \frac{7}{2} + \frac{32 2 - 2}{3}

Decimal

10.91827 \dots

Solution steps

\int_{- 7}^{0} \frac{y}{7} + y + 8 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_{- 7}^{0} \frac{y}{7} d y + \int_{- 7}^{0} y + 8 d y

\int_{- 7}^{0} \frac{y}{7} d y = - \frac{7}{2}

\int_{- 7}^{0} y + 8 d y = \frac{32 2 - 2}{3}

= - \frac{7}{2} + \frac{32 2 - 2}{3}

What is the integral from-7 to 0 of (y/7+sqrt(y+8)) ?
The integral from-7 to 0 of (y/7+sqrt(y+8)) is -7/2+(32sqrt(2)-2)/3