What is the integral from 0 to 2 of (x^3)/2 ?

The integral from 0 to 2 of (x^3)/2 is 2

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integral from 0 to 2 of (x^3)/2

\int_{0}^{2} \frac{x ^{3}}{2} d x

2

Solution steps

\int_{0}^{2} \frac{x ^{3}}{2} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

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

= \frac{1}{2} [\frac{x ^{4}}{4}]_{0}^{2}

Compute the boundaries:

4

= \frac{1}{2} \cdot 4

Simplify

= 2

\frac{\partial}{\partial x} (x e^{x y})

y^{^{'}} = \frac{x y ( 4 - y )}{1 + x}

\frac{d}{d x} (x^{4} - 25 x^{2} + 144)

\frac{\partial}{\partial x} (x (x^{2} + y^{2})^{\frac{1}{2}})

y = 9 e^{9 e^{x} + x}

What is the integral from 0 to 2 of (x^3)/2 ?
The integral from 0 to 2 of (x^3)/2 is 2