What is the integral from-3 to 5 of 2y-(y^2-15) ?

The integral from-3 to 5 of 2y-(y^2-15) is 256/3

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integral from-3 to 5 of 2y-(y^2-15)

\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

\frac{256}{3}

Decimal Notation

85.33333 \dots

Solution steps

\int_{- 3}^{5} 2 y - (y^{2} - 15) d y

Simplify

= \int_{- 3}^{5} 2 y - y^{2} + 15 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_{- 3}^{5} 2 y d y - \int_{- 3}^{5} y^{2} d y + \int_{- 3}^{5} 15 d y

\int_{- 3}^{5} 2 y d y = 16

\int_{- 3}^{5} y^{2} d y = \frac{152}{3}

\int_{- 3}^{5} 15 d y = 120

= 16 - \frac{152}{3} + 120

Simplify

16 - \frac{152}{3} + 120 : \frac{256}{3}

= \frac{256}{3}

\frac{\partial}{\partial x} (3 x arctan (\frac{x}{y}))

4 e^{x} + x

\frac{d y}{d x} = - \frac{2 x}{y}

(x + 1) (4 x^{2} - 4 x - 8)

\frac{\partial}{\partial x} (x^{3} y - x y^{3})

What is the integral from-3 to 5 of 2y-(y^2-15) ?
The integral from-3 to 5 of 2y-(y^2-15) is 256/3