What is the integral from 0 to 1 of 12sqrt(t) ?

The integral from 0 to 1 of 12sqrt(t) is 8

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integral from 0 to 1 of 12sqrt(t)

\int_{0}^{1} 12 t d t

8

Solution steps

\int_{0}^{1} 12 t d t

Take the constant out:

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

= 12 \cdot \int_{0}^{1} t d t

Apply the Power Rule

: [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{1}

= 12 [\frac{2}{3} t^{\frac{3}{2}}]_{0}^{1}

Compute the boundaries:

\frac{2}{3}

= 12 \cdot \frac{2}{3}

Simplify

= 8

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What is the integral from 0 to 1 of 12sqrt(t) ?
The integral from 0 to 1 of 12sqrt(t) is 8