What is the integral from 2 to 7 of 4x ?

The integral from 2 to 7 of 4x is 90

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integral from 2 to 7 of 4x

\int_{2}^{7} 4 x d x

90

Solution steps

\int_{2}^{7} 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}^{7} x d x

Apply the Power Rule

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

= 4 [\frac{x ^{2}}{2}]_{2}^{7}

Compute the boundaries:

\frac{45}{2}

= 4 \cdot \frac{45}{2}

Simplify

= 90

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