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

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

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integral from 1 to 2 of 2(x-1)

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

1

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{1}^{2} x - 1 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

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

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

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

= 2 (\frac{3}{2} - 1)

Simplify

2 (\frac{3}{2} - 1) : 1

= 1

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