What is the integral from 7 to-5 of g(x) ?

The integral from 7 to-5 of g(x) is -g*12

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integral from 7 to-5 of g(x)

\int_{7}^{- 5} g (x) d x

- g \cdot 12

Solution steps

\int_{7}^{- 5} gx d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{- 5}^{7} gx d x

Take the constant out:

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

= - g \cdot \int_{- 5}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{- 5}^{7}

= - g [\frac{x ^{2}}{2}]_{- 5}^{7}

Compute the boundaries:

12

= - g \cdot 12

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What is the integral from 7 to-5 of g(x) ?
The integral from 7 to-5 of g(x) is -g*12