What is the integral from 0 to 1 of 2z ?

The integral from 0 to 1 of 2z is 1

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integral from 0 to 1 of 2z

\int_{0}^{1} 2 z d z

1

Solution steps

\int_{0}^{1} 2 z d z

Take the constant out:

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

= 2 \cdot \int_{0}^{1} z d z

Apply the Power Rule

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

Compute the boundaries:

\frac{1}{2}

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

Simplify

= 1