What is the integral from 2 to 8 of 3x ?

The integral from 2 to 8 of 3x is 90

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integral from 2 to 8 of 3x

\int_{2}^{8} 3 x d x

90

Solution steps

\int_{2}^{8} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{2}^{8} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{2}^{8}

= 3 [\frac{x ^{2}}{2}]_{2}^{8}

Compute the boundaries:

30

= 3 \cdot 30

Simplify

= 90

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