What is the integral from 0 to 8 of-x^2+2x+4 ?

The integral from 0 to 8 of-x^2+2x+4 is -224/3

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integral from 0 to 8 of-x^2+2x+4

\int_{0}^{8} - x^{2} + 2 x + 4 d x

- \frac{224}{3}

Decimal Notation

- 74.66666 \dots

Solution steps

\int_{0}^{8} - x^{2} + 2 x + 4 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_{0}^{8} x^{2} d x + \int_{0}^{8} 2 x d x + \int_{0}^{8} 4 d x

\int_{0}^{8} x^{2} d x = \frac{512}{3}

\int_{0}^{8} 2 x d x = 64

\int_{0}^{8} 4 d x = 32

= - \frac{512}{3} + 64 + 32

Simplify

- \frac{512}{3} + 64 + 32 : - \frac{224}{3}

= - \frac{224}{3}

f (x) = \frac{4 x}{x + 1}, at x = 3

x \to - 4 lim (\frac{∣ x + 4 ∣}{x + 4})

y = (e^{4 x} - 3)^{8}

\frac{d ^{3}}{d x ^{3}} (2 x^{3} - 4 x^{2} + 2)

x^{3} - 5 x, 4 x

What is the integral from 0 to 8 of-x^2+2x+4 ?
The integral from 0 to 8 of-x^2+2x+4 is -224/3