What is the integral from 1 to 3 of 8x ?

The integral from 1 to 3 of 8x is 32

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integral from 1 to 3 of 8x

\int_{1}^{3} 8 x d x

32

Solution steps

\int_{1}^{3} 8 x d x

Take the constant out:

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

= 8 \cdot \int_{1}^{3} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{3}

= 8 [\frac{x ^{2}}{2}]_{1}^{3}

Compute the boundaries:

4

= 8 \cdot 4

Simplify

= 32

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