What is the integral from-6 to 0 of (y/6+sqrt(y+7)) ?

The integral from-6 to 0 of (y/6+sqrt(y+7)) is -3+(14sqrt(7)-2)/3

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integral from-6 to 0 of (y/6+sqrt(y+7))

\int_{- 6}^{0} (\frac{y}{6} + y + 7) d y

- 3 + \frac{14 7 - 2}{3}

Decimal

8.68017 \dots

Solution steps

\int_{- 6}^{0} \frac{y}{6} + y + 7 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_{- 6}^{0} \frac{y}{6} d y + \int_{- 6}^{0} y + 7 d y

\int_{- 6}^{0} \frac{y}{6} d y = - 3

\int_{- 6}^{0} y + 7 d y = \frac{14 7 - 2}{3}

= - 3 + \frac{14 7 - 2}{3}

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What is the integral from-6 to 0 of (y/6+sqrt(y+7)) ?
The integral from-6 to 0 of (y/6+sqrt(y+7)) is -3+(14sqrt(7)-2)/3