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}

2 x^{\frac{3}{2}}

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\int 2 x sin (2 x) d x

\int - k x e^{- k x} d x

\frac{\partial}{\partial x} (cos (x + y))

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