What is the integral from 2 to 0 of 2x ?

The integral from 2 to 0 of 2x is -4

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integral from 2 to 0 of 2x

\int_{2}^{0} 2 x d x

- 4

Solution steps

\int_{2}^{0} 2 x d x

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

= - \int_{0}^{2} 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_{0}^{2} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{2}

= - 2 [\frac{x ^{2}}{2}]_{0}^{2}

Compute the boundaries:

2

= - 2 \cdot 2

Simplify

= - 4

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