What is the integral from 3 to x of 9x ?

The integral from 3 to x of 9x is (9(x^2-9))/2

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integral from 3 to x of 9x

\int_{3}^{x} 9 x d x

\frac{9 ( x ^{2} - 9 )}{2}

Solution steps

\int_{3}^{x} 9 x d x

Take the constant out:

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

= 9 \cdot \int_{3}^{x} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{3}^{x}

= 9 [\frac{x ^{2}}{2}]_{3}^{x}

Compute the boundaries:

\frac{x ^{2}}{2} - \frac{9}{2}

= 9 (\frac{x ^{2}}{2} - \frac{9}{2})

Simplify

= \frac{9 ( x ^{2} - 9 )}{2}

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What is the integral from 3 to x of 9x ?
The integral from 3 to x of 9x is (9(x^2-9))/2