What is the integral from 0 to 10 of 0.5q+25 ?

The integral from 0 to 10 of 0.5q+25 is 275

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integral from 0 to 10 of 0.5q+25

\int_{0}^{10} 0.5 q + 25 d q

275

Solution steps

\int_{0}^{10} 0.5 q + 25 d q

Apply u-substitution

: \int_{25}^{30} \frac{u}{0.5} d u

= \int_{25}^{30} \frac{u}{0.5} d u

Take the constant out:

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

= \frac{1}{0.5} \cdot \int_{25}^{30} u d u

Simplify

= 2 \cdot \int_{25}^{30} u d u

Apply the Power Rule

: [\frac{u ^{2}}{2}]_{25}^{30}

= 2 [\frac{u ^{2}}{2}]_{25}^{30}

Compute the boundaries:

\frac{275}{2}

= 2 \cdot \frac{275}{2}

Simplify

= 275

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What is the integral from 0 to 10 of 0.5q+25 ?
The integral from 0 to 10 of 0.5q+25 is 275