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

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

Popular >

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

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

- \frac{253}{6}

Decimal

- 42.16666 \dots

Solution steps

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

Expand

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

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

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} u^{2} d u - \int_{0}^{1} u d u - \int_{0}^{1} 42 d u

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

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

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

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

Simplify

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

= - \frac{253}{6}

8 y^{^{''}} + 8 y^{^{'}} + \frac{1}{4} y = 0, y (0) = 2, y^{^{'}} (0) = 1

\int 6 x^{9} e^{- x^{5}} d x

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

\int \frac{1}{1 - e ^{2 x}} d x

\frac{d}{d x} (2 lo g_{6} (x))

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