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Popular Calculus >

integral from 0 to x of (2-x)

Solution

\int_{0}^{x} (2 - x) d x

Solution

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

Solution steps

\int_{0}^{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_{0}^{x} 2 d x - \int_{0}^{x} x d x

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

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

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

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Frequently Asked Questions (FAQ)

What is the integral from 0 to x of (2-x) ?
The integral from 0 to x of (2-x) is 2x-(x^2)/2