What is the integral from 0 to 2 of 6x ?

The integral from 0 to 2 of 6x is 12

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integral from 0 to 2 of 6x

\int_{0}^{2} 6 x d x

12

Solution steps

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

Apply the Power Rule

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

= 6 [\frac{x ^{2}}{2}]_{0}^{2}

Compute the boundaries:

2

= 6 \cdot 2

Simplify

= 12

\int sec (8 x) tan (8 x) d x

(\frac{- x ^{2} - 4 x}{( x ^{2} - x - 2 ) ^{2}})^{^{'}}

x \to 3 lim (x - 2)

\frac{d}{d x} (C e^{4 x})

\frac{d}{d x} ((x^{\frac{2}{3}}) (6 - x)^{\frac{1}{3}})