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

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

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

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

\frac{125}{6}

Decimal Notation

20.83333 \dots

Solution steps

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

Simplify

= \int_{- 2}^{3} y - y^{2} + 6 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_{- 2}^{3} y d y - \int_{- 2}^{3} y^{2} d y + \int_{- 2}^{3} 6 d y

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

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

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

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

Simplify

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

= \frac{125}{6}

\int_{- 2}^{2} \frac{8}{x ^{2} + 4} d x

\int_{- 1}^{3} - x^{3} - 5 x + 1 d x

\int_{- 1}^{1} (2 x^{2} + 7) d x

\int_{- 1}^{2} 2 x^{3} - 8 x^{2} + 2 x + 12 d x

\int_{- 2}^{2} x^{2} - 3 x + 5 d x

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