What is the integral from 1 to 2 of 5x ?

The integral from 1 to 2 of 5x is 15/2

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integral from 1 to 2 of 5x

\int_{1}^{2} 5 x d x

\frac{15}{2}

Decimal

7.5

Solution steps

\int_{1}^{2} 5 x d x

Take the constant out:

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

= 5 \cdot \int_{1}^{2} x d x

Apply the Power Rule

= 5 [\frac{x ^{2}}{2}]_{1}^{2}

Compute the boundaries:

\frac{3}{2}

= 5 \cdot \frac{3}{2}

Simplify

= \frac{15}{2}