What is the integral from 0 to 2 of (2x+2-x^2-2) ?

The integral from 0 to 2 of (2x+2-x^2-2) is 4/3

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integral from 0 to 2 of (2x+2-x^2-2)

\int_{0}^{2} (2 x + 2 - x^{2} - 2) d x

\frac{4}{3}

Decimal Notation

1.33333 \dots

Solution steps

\int_{0}^{2} 2 x + 2 - x^{2} - 2 d x

Simplify

= \int_{0}^{2} - x^{2} + 2 x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{0}^{2} x^{2} d x + \int_{0}^{2} 2 x d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 2 x d x = 4

= - \frac{8}{3} + 4

Simplify

- \frac{8}{3} + 4 : \frac{4}{3}

= \frac{4}{3}

x \to \infty lim (\frac{ln ( x ^{2} - x + 1 )}{ln ( x ^{10} + x + 1 )})

\frac{\partial}{\partial x} (3 sin (2 x))

\int \frac{1}{3 - x} d x

\frac{\partial}{\partial y} (2 y^{3} - 3 y^{2} - 12 y + 6)

(x^{2} + 1) y^{^{'}} + 8 x (y - 1) = 0, y (0) = 4

What is the integral from 0 to 2 of (2x+2-x^2-2) ?
The integral from 0 to 2 of (2x+2-x^2-2) is 4/3