What is the integral from 3 to 5 of (-x^2+8x-12) ?

The integral from 3 to 5 of (-x^2+8x-12) is 22/3

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integral from 3 to 5 of (-x^2+8x-12)

\int_{3}^{5} (- x^{2} + 8 x - 12) d x

\frac{22}{3}

Decimal Notation

7.33333 \dots

Solution steps

\int_{3}^{5} - x^{2} + 8 x - 12 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_{3}^{5} x^{2} d x + \int_{3}^{5} 8 x d x - \int_{3}^{5} 12 d x

\int_{3}^{5} x^{2} d x = \frac{98}{3}

\int_{3}^{5} 8 x d x = 64

\int_{3}^{5} 12 d x = 24

= - \frac{98}{3} + 64 - 24

Simplify

- \frac{98}{3} + 64 - 24 : \frac{22}{3}

= \frac{22}{3}

x \to 2 lim (3 x + 6)

\int (x^{2} + 1) (x^{3} + 3 x) d x

\frac{d}{d x} (8 e^{2})

n = 1 \sum \infty \frac{1}{n ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{87 x}{99 x - 87})

What is the integral from 3 to 5 of (-x^2+8x-12) ?
The integral from 3 to 5 of (-x^2+8x-12) is 22/3