What is the integral from 1 to 3 of-2x ?

The integral from 1 to 3 of-2x is -8

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integral from 1 to 3 of-2x

\int_{1}^{3} - 2 x d x

- 8

Solution steps

\int_{1}^{3} - 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_{1}^{3} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{1}^{3}

= - 2 [\frac{x ^{2}}{2}]_{1}^{3}

Compute the boundaries:

4

= - 2 \cdot 4

Simplify

= - 8

\int_{1}^{4} 5^{2 x} d x

\int_{0}^{\frac{1}{2}} (2 x) d x

\int_{- 1}^{2} 9 - x^{2} d x

\int_{1}^{10} \frac{20}{x} d x

\int_{- 2}^{3} 9 - x^{2} d x