What is the integral from-5 to 0 of (y/5+sqrt(y+6)) ?

The integral from-5 to 0 of (y/5+sqrt(y+6)) is 4sqrt(6)-19/6

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integral from-5 to 0 of (y/5+sqrt(y+6))

\int_{- 5}^{0} (\frac{y}{5} + y + 6) d y

46 - \frac{19}{6}

Decimal Notation

6.63129 \dots

Solution steps

\int_{- 5}^{0} \frac{y}{5} + y + 6 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_{- 5}^{0} \frac{y}{5} d y + \int_{- 5}^{0} y + 6 d y

\int_{- 5}^{0} \frac{y}{5} d y = - \frac{5}{2}

\int_{- 5}^{0} y + 6 d y = 46 - \frac{2}{3}

= - \frac{5}{2} + 46 - \frac{2}{3}

Simplify

- \frac{5}{2} + 46 - \frac{2}{3} : 46 - \frac{19}{6}

= 46 - \frac{19}{6}

\frac{d y}{d x}, x y = 84

x \to 2 lim (2 x^{2} + 5 x + 2)

\frac{d}{d x} (e^{- s i n (x)})

\int \frac{( x - 5 ) ^{2}}{x ^{3}} d x

\frac{d}{d x} (\frac{1}{x - ( x ^{2} - 1 ) ^{\frac{1}{2}}})

What is the integral from-5 to 0 of (y/5+sqrt(y+6)) ?
The integral from-5 to 0 of (y/5+sqrt(y+6)) is 4sqrt(6)-19/6