What is the integral from 0 to 2 of 1/2 x^3 ?

The integral from 0 to 2 of 1/2 x^3 is 2

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integral from 0 to 2 of 1/2 x^3

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

2

Solution steps

\int_{0}^{2} \frac{1}{2} x^{3} 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

\int_{1}^{5} 2 π y (5 - y) d y

\int_{- 3}^{3} (2 - x)^{5} d x

\int_{1}^{7} \frac{6}{x ^{4}} d x

\int_{0}^{π} 2 \cdot sin (x) d x

\int_{0}^{2 π} 5 x 2 d x

What is the integral from 0 to 2 of 1/2 x^3 ?
The integral from 0 to 2 of 1/2 x^3 is 2