What is the integral from-3 to 2 of (6-x-x^2) ?

The integral from-3 to 2 of (6-x-x^2) is 125/6

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integral from-3 to 2 of (6-x-x^2)

\int_{- 3}^{2} (6 - x - x^{2}) d x

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

\int_{- 3}^{2} 6 - x - x^{2} 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_{- 3}^{2} 6 d x - \int_{- 3}^{2} x d x - \int_{- 3}^{2} x^{2} d x

\int_{- 3}^{2} 6 d x = 30

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

\int_{- 3}^{2} x^{2} d x = \frac{35}{3}

= 30 - (- \frac{5}{2}) - \frac{35}{3}

Simplify

30 - (- \frac{5}{2}) - \frac{35}{3} : \frac{125}{6}

= \frac{125}{6}

\frac{d}{d x} (e^{2 s i n^{2} (x)})

\int (\frac{2}{x ^{3}}) d x

f (x) = 4 x - 4 x

\frac{\partial}{\partial x} (cos (- x))

\frac{d}{d x} (14 - x)

What is the integral from-3 to 2 of (6-x-x^2) ?
The integral from-3 to 2 of (6-x-x^2) is 125/6