What is the integral from 0 to 2 of 1/4 x^3 ?

The integral from 0 to 2 of 1/4 x^3 is 1

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integral from 0 to 2 of 1/4 x^3

\int_{0}^{2} \frac{1}{4} x^{3} d x

1

Solution steps

\int_{0}^{2} \frac{1}{4} x^{3} d x

Take the constant out:

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

= \frac{1}{4} \cdot \int_{0}^{2} x^{3} d x

Apply the Power Rule

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

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

Compute the boundaries:

4

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

Simplify

= 1

\int_{1}^{4} (2 - x) - (- x) d x

\int_{0}^{π} 8 cos (x) d x

\int_{0}^{1} π (1 - y) d y

\int_{4}^{9} x^{3} d x

\int_{1}^{2} x^{2} - 3 d x

What is the integral from 0 to 2 of 1/4 x^3 ?
The integral from 0 to 2 of 1/4 x^3 is 1