What is the integral from 1 to 8 of (1-x)(x-8) ?

The integral from 1 to 8 of (1-x)(x-8) is 343/6

Popular >

integral from 1 to 8 of (1-x)(x-8)

\int_{1}^{8} (1 - x) (x - 8) d x

\frac{343}{6}

Decimal Notation

57.16666 \dots

Solution steps

\int_{1}^{8} (1 - x) (x - 8) d x

Expand

(1 - x) (x - 8) : 9 x - x^{2} - 8

= \int_{1}^{8} 9 x - x^{2} - 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_{1}^{8} 9 x d x - \int_{1}^{8} x^{2} d x - \int_{1}^{8} 8 d x

\int_{1}^{8} 9 x d x = \frac{567}{2}

\int_{1}^{8} x^{2} d x = \frac{511}{3}

\int_{1}^{8} 8 d x = 56

= \frac{567}{2} - \frac{511}{3} - 56

Simplify

\frac{567}{2} - \frac{511}{3} - 56 : \frac{343}{6}

= \frac{343}{6}

\int_{0}^{3} (3 t - 1)^{54} d t

\int_{0}^{3} t d t

\int_{0}^{1} \frac{1}{1 + 4 x ^{2}} d x

\int_{0}^{6} 4 x - x^{2} d x

\int_{0}^{2} 8 - x^{3} d x

What is the integral from 1 to 8 of (1-x)(x-8) ?
The integral from 1 to 8 of (1-x)(x-8) is 343/6