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

The integral from 2 to 4 of (-x^2+2x+8) is 28/3

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integral from 2 to 4 of (-x^2+2x+8)

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

\frac{28}{3}

Decimal Notation

9.33333 \dots

Solution steps

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

\int_{2}^{4} x^{2} d x = \frac{56}{3}

\int_{2}^{4} 2 x d x = 12

\int_{2}^{4} 8 d x = 16

= - \frac{56}{3} + 12 + 16

Simplify

- \frac{56}{3} + 12 + 16 : \frac{28}{3}

= \frac{28}{3}

\int_{0}^{1} (x^{12} + 1 2^{x}) d x

\int_{0}^{1} x^{4} - x^{5} d x

\int_{1}^{3} x^{2} + 3 d x

\int_{1}^{4} 3^{x - 1} d x

\int_{1}^{3} \frac{5}{x} d x

What is the integral from 2 to 4 of (-x^2+2x+8) ?
The integral from 2 to 4 of (-x^2+2x+8) is 28/3