What is the integral from 2 to 5 of 4x ?

The integral from 2 to 5 of 4x is 42

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integral from 2 to 5 of 4x

\int_{2}^{5} 4 x d x

42

Solution steps

\int_{2}^{5} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{2}^{5} x d x

Apply the Power Rule

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

= 4 [\frac{x ^{2}}{2}]_{2}^{5}

Compute the boundaries:

\frac{21}{2}

= 4 \cdot \frac{21}{2}

Simplify

= 42

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