What is the integral from 1 to 3 of 6x ?

The integral from 1 to 3 of 6x is 24

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integral from 1 to 3 of 6x

\int_{1}^{3} 6 x d x

24

Solution steps

\int_{1}^{3} 6 x d x

Take the constant out:

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

= 6 \cdot \int_{1}^{3} x d x

Apply the Power Rule

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

= 6 [\frac{x ^{2}}{2}]_{1}^{3}

Compute the boundaries:

4

= 6 \cdot 4

Simplify

= 24

\int_{- 1}^{2} \frac{1}{x + 2} d x

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