What is the integral from 0 to 4 of 2x ?

The integral from 0 to 4 of 2x is 16

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integral from 0 to 4 of 2x

\int_{0}^{4} 2 x d x

16

Solution steps

\int_{0}^{4} 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_{0}^{4} x d x

Apply the Power Rule

: [\frac{x ^{2}}{2}]_{0}^{4}

= 2 [\frac{x ^{2}}{2}]_{0}^{4}

Compute the boundaries:

8

= 2 \cdot 8

Simplify

= 16

y^{^{''}} - 4 y^{^{'}} = 7 x + 1

\frac{\partial}{\partial x} (e^{4 x} cos (7 y))

\frac{d}{d y} (y^{- 1})

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

x \to 0 lim (x \cdot arctan (\frac{1}{x}))