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

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

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integral from 1 to x of (2-x)

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

2 x - 2 - \frac{x ^{2} - 1}{2}

Solution steps

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

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

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

= 2 x - 2 - \frac{x ^{2} - 1}{2}

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