What is the integral from 2 to 6 of 1/8 (x-2) ?

The integral from 2 to 6 of 1/8 (x-2) is 1

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integral from 2 to 6 of 1/8 (x-2)

\int_{2}^{6} \frac{1}{8} (x - 2) d x

1

Solution steps

\int_{2}^{6} \frac{1}{8} (x - 2) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{8} \cdot \int_{2}^{6} x - 2 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

= \frac{1}{8} (\int_{2}^{6} x d x - \int_{2}^{6} 2 d x)

\int_{2}^{6} x d x = 16

\int_{2}^{6} 2 d x = 8

= \frac{1}{8} (16 - 8)

Simplify

\frac{1}{8} (16 - 8) : 1

= 1

2 e^{2 x + 1}

\int e^{x - 1} d x

\int_{1}^{2} \frac{x - 4}{x ^{2}} d x

\int_{0}^{1} (5 x^{4} - 4 x^{3}) d x

g (x) = 2 x^{2}

What is the integral from 2 to 6 of 1/8 (x-2) ?
The integral from 2 to 6 of 1/8 (x-2) is 1