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 Notation

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}

\int sin^{2} (3 x) cos^{2} (3 x) d x

\frac{( 2 x ^{2} + 16 x + x ^{3^{\frac{1}{2}}} + 5 )}{x ^{3}}

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

y = x^{4} + 9 x^{2} - x, (1, 9)

\int_{1}^{e} \frac{ln ( z )}{z ^{2}} d z

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