What is the integral from 1 to 12 of (1-x)(x-12) ?

The integral from 1 to 12 of (1-x)(x-12) is 1331/6

Popular >

integral from 1 to 12 of (1-x)(x-12)

\int_{1}^{12} (1 - x) (x - 12) d x

\frac{1331}{6}

Decimal

221.83333 \dots

Solution steps

\int_{1}^{12} (1 - x) (x - 12) d x

Expand

(1 - x) (x - 12) : 13 x - x^{2} - 12

= \int_{1}^{12} 13 x - x^{2} - 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_{1}^{12} 13 x d x - \int_{1}^{12} x^{2} d x - \int_{1}^{12} 12 d x

\int_{1}^{12} 13 x d x = \frac{1859}{2}

\int_{1}^{12} x^{2} d x = \frac{1727}{3}

\int_{1}^{12} 12 d x = 132

= \frac{1859}{2} - \frac{1727}{3} - 132

Simplify

\frac{1859}{2} - \frac{1727}{3} - 132 : \frac{1331}{6}

= \frac{1331}{6}

\int_{2}^{3} 32 x - 63 d x

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

\int_{- 1}^{2} π (\frac{x ^{3}}{4} + 1)^{2} d x

\int_{0}^{1} 2 x d x

\int_{3}^{5} 6 x^{2} (x^{3} + 4) d x

What is the integral from 1 to 12 of (1-x)(x-12) ?
The integral from 1 to 12 of (1-x)(x-12) is 1331/6