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

The integral from 4 to 2 of 2x is -12

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integral from 4 to 2 of 2x

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

- 12

Solution steps

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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{2}^{4} 2 x d x

Take the constant out:

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

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

Apply the Power Rule

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

Compute the boundaries:

6

= - 2 \cdot 6

Simplify

= - 12