What is the integral from 3 to 7 of 7x ?

The integral from 3 to 7 of 7x is 140

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integral from 3 to 7 of 7x

\int_{3}^{7} 7 x d x

140

Solution steps

\int_{3}^{7} 7 x d x

Take the constant out:

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

= 7 \cdot \int_{3}^{7} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{3}^{7}

= 7 [\frac{x ^{2}}{2}]_{3}^{7}

Compute the boundaries:

20

= 7 \cdot 20

Simplify

= 140

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