What is the integral from-3 to 2 of-2x ?

The integral from-3 to 2 of-2x is 5

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integral from-3 to 2 of-2x

\int_{- 3}^{2} - 2 x d x

5

Solution steps

\int_{- 3}^{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_{- 3}^{2} x d x

Apply the Power Rule

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

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

Compute the boundaries:

- \frac{5}{2}

= - 2 (- \frac{5}{2})

Simplify

= 5

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