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

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

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

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

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{125}{6}

\int (3 y^{2} + 6 y) (y^{3} + 3 y^{2} + 1)^{\frac{2}{3}} d y

f (x) = x^{2} - 8

\frac{d}{d x} (\frac{x + 3}{∣ x + 3 ∣})

x \to 0 + lim (\frac{( ln ( x ) ) ^{2}}{x})

\frac{\partial}{\partial x} (sin^{4} (x))

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