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 Notation

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}

y = x^{2} - 4 x, y = 4 x

\int \frac{e ^{2 x}}{e ^{2 x} + 4} d x

x \to 0 lim (\frac{2 ^{3 + x} - 8}{x})

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

\frac{d}{d x} (5 + 7 x)

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