What is the integral from 0 to 5 of 2(11+0.5x) ?

The integral from 0 to 5 of 2(11+0.5x) is 122.5

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integral from 0 to 5 of 2(11+0.5x)

\int_{0}^{5} 2 (11 + 0.5 x) d x

122.5

Solution steps

\int_{0}^{5} 2 (11 + 0.5 x) d x

Take the constant out:

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

= 2 \cdot \int_{0}^{5} 11 + 0.5 x d x

Apply u-substitution

= 2 \cdot \int_{11}^{13.5} \frac{u}{0.5} d u

Take the constant out:

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

= 2 \cdot \frac{1}{0.5} \cdot \int_{11}^{13.5} u d u

Simplify

= 2 \cdot 2 \cdot \int_{11}^{13.5} u d u

Apply the Power Rule

= 2 \cdot 2 [\frac{u ^{2}}{2}]_{11}^{13.5}

Simplify

= 4 [0.5 u^{2}]_{11}^{13.5}

Compute the boundaries:

30.625

= 4 \cdot 30.625

Simplify

= 122.5

What is the integral from 0 to 5 of 2(11+0.5x) ?
The integral from 0 to 5 of 2(11+0.5x) is 122.5