What is the integral from 0 to 3 of 4x ?

The integral from 0 to 3 of 4x is 18

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integral from 0 to 3 of 4x

\int_{0}^{3} 4 x d x

18

Solution steps

\int_{0}^{3} 4 x d x

Take the constant out:

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

= 4 \cdot \int_{0}^{3} x d x

Apply the Power Rule

= 4 [\frac{x ^{2}}{2}]_{0}^{3}

Compute the boundaries:

\frac{9}{2}

= 4 \cdot \frac{9}{2}

Simplify

= 18

(2 x + y) d x + (x - 2 y) d y = 0

f (x) = 4 x^{2} ln (4 x)

\frac{d}{d x} (2 x - 5 y + 3)

\frac{d y}{d x} = e^{6 x + 5 y}

\frac{d}{d x} (\frac{x ^{5}}{1 - x ^{4}})