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

The integral from 0 to 4 of 3x is 24

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integral from 0 to 4 of 3x

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

24

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Compute the boundaries:

8

= 3 \cdot 8

Simplify

= 24

\int x^{2} 36 - x^{2} d x

n = 2 \sum \infty n^{2}

\frac{d}{d x} (a x^{2} + ∣ x ∣^{3})

\frac{\partial}{\partial z} (x cos (\frac{y}{z}))

\frac{d}{d x} (c_{1} e^{- 4 x} + c_{2} x e^{- 4 x})