What is the integral from-2 to 2 of (6x)-(x^2-7) ?

The integral from-2 to 2 of (6x)-(x^2-7) is 68/3

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integral from-2 to 2 of (6x)-(x^2-7)

\int_{- 2}^{2} (6 x) - (x^{2} - 7) d x

\frac{68}{3}

Decimal

22.66666 \dots

Solution steps

\int_{- 2}^{2} 6 x - (x^{2} - 7) d x

Simplify

= \int_{- 2}^{2} 6 x - x^{2} + 7 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_{- 2}^{2} 6 x d x - \int_{- 2}^{2} x^{2} d x + \int_{- 2}^{2} 7 d x

\int_{- 2}^{2} 6 x d x = 0

\int_{- 2}^{2} x^{2} d x = \frac{16}{3}

\int_{- 2}^{2} 7 d x = 28

= 0 - \frac{16}{3} + 28

Simplify

0 - \frac{16}{3} + 28 : \frac{68}{3}

= \frac{68}{3}

What is the integral from-2 to 2 of (6x)-(x^2-7) ?
The integral from-2 to 2 of (6x)-(x^2-7) is 68/3