What is the integral from-1 to 2 of (y+2-y^2) ?

The integral from-1 to 2 of (y+2-y^2) is 9/2

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integral from-1 to 2 of (y+2-y^2)

\int_{- 1}^{2} (y + 2 - y^{2}) d y

\frac{9}{2}

Solution steps

\int_{- 1}^{2} y + 2 - y^{2} 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_{- 1}^{2} y d y + \int_{- 1}^{2} 2 d y - \int_{- 1}^{2} y^{2} d y

\int_{- 1}^{2} y d y = \frac{3}{2}

\int_{- 1}^{2} 2 d y = 6

\int_{- 1}^{2} y^{2} d y = 3

= \frac{3}{2} + 6 - 3

Simplify

\frac{3}{2} + 6 - 3 : \frac{9}{2}

= \frac{9}{2}

\frac{e ^{\frac{- π}{2}}}{s ^{2} + 9}

\frac{\partial}{\partial x} (x^{3} + x^{2} y - 4 y^{3})

x (\frac{d y}{d x}) + y = 3 x y^{2}

\int 7 tan^{3} (x) sec (x) d x

What is the integral from-1 to 2 of (y+2-y^2) ?
The integral from-1 to 2 of (y+2-y^2) is 9/2