What is the integral from 10 to 7 of g(x) ?

The integral from 10 to 7 of g(x) is -(51g)/2

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integral from 10 to 7 of g(x)

\int_{10}^{7} g (x) d x

- \frac{51 g}{2}

Solution steps

\int_{10}^{7} gx d x

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

= - \int_{7}^{10} gx d x

Take the constant out:

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

= - g \cdot \int_{7}^{10} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{7}^{10}

= - g [\frac{x ^{2}}{2}]_{7}^{10}

Compute the boundaries:

\frac{51}{2}

= - g \frac{51}{2}

Simplify

= - \frac{51 g}{2}

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What is the integral from 10 to 7 of g(x) ?
The integral from 10 to 7 of g(x) is -(51g)/2