What is the integral from-4 to 0 of (y/4+sqrt(y+5)) ?

The integral from-4 to 0 of (y/4+sqrt(y+5)) is -2+(10sqrt(5)-2)/3

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integral from-4 to 0 of (y/4+sqrt(y+5))

\int_{- 4}^{0} (\frac{y}{4} + y + 5) d y

- 2 + \frac{10 5 - 2}{3}

Decimal

4.78689 \dots

Solution steps

\int_{- 4}^{0} \frac{y}{4} + y + 5 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_{- 4}^{0} \frac{y}{4} d y + \int_{- 4}^{0} y + 5 d y

\int_{- 4}^{0} \frac{y}{4} d y = - 2

\int_{- 4}^{0} y + 5 d y = \frac{10 5 - 2}{3}

= - 2 + \frac{10 5 - 2}{3}

What is the integral from-4 to 0 of (y/4+sqrt(y+5)) ?
The integral from-4 to 0 of (y/4+sqrt(y+5)) is -2+(10sqrt(5)-2)/3