What is the integral from 4 to 5 of 3x ?

The integral from 4 to 5 of 3x is 27/2

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integral from 4 to 5 of 3x

\int_{4}^{5} 3 x d x

\frac{27}{2}

Decimal

13.5

Solution steps

\int_{4}^{5} 3 x d x

Take the constant out:

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

= 3 \cdot \int_{4}^{5} x d x

Apply the Power Rule

= 3 [\frac{x ^{2}}{2}]_{4}^{5}

Compute the boundaries:

\frac{9}{2}

= 3 \cdot \frac{9}{2}

Simplify

= \frac{27}{2}