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

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

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integral from-2 to 0 of y/2+sqrt(y+3)

\int_{- 2}^{0} \frac{y}{2} + y + 3 d y

23 - \frac{5}{3}

Decimal

1.79743 \dots

Solution steps

\int_{- 2}^{0} \frac{y}{2} + y + 3 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_{- 2}^{0} \frac{y}{2} d y + \int_{- 2}^{0} y + 3 d y

\int_{- 2}^{0} \frac{y}{2} d y = - 1

\int_{- 2}^{0} y + 3 d y = 23 - \frac{2}{3}

= - 1 + 23 - \frac{2}{3}

Combine the fractions

- 1 - \frac{2}{3} : - \frac{5}{3}

= 23 - \frac{5}{3}

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