What is the integral from 0 to 1 of (x+6)(x-7) ?

The integral from 0 to 1 of (x+6)(x-7) is -253/6

Popular >

integral from 0 to 1 of (x+6)(x-7)

\int_{0}^{1} (x + 6) (x - 7) d x

- \frac{253}{6}

Decimal Notation

- 42.16666 \dots

Solution steps

\int_{0}^{1} (x + 6) (x - 7) d x

Expand

(x + 6) (x - 7) : x^{2} - x - 42

= \int_{0}^{1} x^{2} - x - 42 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}^{1} x^{2} d x - \int_{0}^{1} x d x - \int_{0}^{1} 42 d x

\int_{0}^{1} x^{2} d x = \frac{1}{3}

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

\int_{0}^{1} 42 d x = 42

= \frac{1}{3} - \frac{1}{2} - 42

Simplify

\frac{1}{3} - \frac{1}{2} - 42 : - \frac{253}{6}

= - \frac{253}{6}

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

\frac{d y}{d x} = \frac{e ^{x}}{y + 2}

\frac{\partial}{\partial x} (x^{2} - 7 x + 12)

\int \frac{x}{x ^{4} - 16} d x

What is the integral from 0 to 1 of (x+6)(x-7) ?
The integral from 0 to 1 of (x+6)(x-7) is -253/6