What is the integral from 4 to 6 of 2x ?

The integral from 4 to 6 of 2x is 20

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integral from 4 to 6 of 2x

\int_{4}^{6} 2 x d x

20

Solution steps

\int_{4}^{6} 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_{4}^{6} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{4}^{6}

= 2 [\frac{x ^{2}}{2}]_{4}^{6}

Compute the boundaries:

10

= 2 \cdot 10

Simplify

= 20

x^{3} - 4 x^{2} + 4 x, [0, 3]

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

\frac{d}{d x} (- 2 x^{2} + 4 x - 4)

\int \frac{1}{16 - x} d x