What is the integral of ((7-x)/(-3)) ?

The integral of ((7-x)/(-3)) is -1/3 (7x-(x^2)/2)+C

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integral of ((7-x)/(-3))

\int (\frac{7 - x}{- 3}) d x

- \frac{1}{3} (7 x - \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{7 - x}{- 3} d x

Take the constant out:

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

= \frac{1}{- 3} \cdot \int 7 - x d x

Simplify

= (- \frac{1}{3}) \cdot \int 7 - 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

= (- \frac{1}{3}) (\int 7 d x - \int x d x)

\int 7 d x = 7 x

\int x d x = \frac{x ^{2}}{2}

= (- \frac{1}{3}) (7 x - \frac{x ^{2}}{2})

Simplify

= - \frac{1}{3} (7 x - \frac{x ^{2}}{2})

Add a constant to the solution

= - \frac{1}{3} (7 x - \frac{x ^{2}}{2}) + C

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What is the integral of ((7-x)/(-3)) ?
The integral of ((7-x)/(-3)) is -1/3 (7x-(x^2)/2)+C