What is the integral from 0 to 7 of sqrt(25-3x) ?

The integral from 0 to 7 of sqrt(25-3x) is 26

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integral from 0 to 7 of sqrt(25-3x)

\int_{0}^{7} 25 - 3 x d x

26

Solution steps

\int_{0}^{7} 25 - 3 x d x

Apply u-substitution

= \int_{25}^{4} - \frac{u}{3} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{4}^{25} - \frac{u}{3} d u

Take the constant out:

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

= - (- \frac{1}{3} \cdot \int_{4}^{25} u d u)

Apply the Power Rule

= - (- \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{25})

Simplify

= \frac{1}{3} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{25}

Compute the boundaries:

78

= \frac{1}{3} \cdot 78

Simplify

= 26

What is the integral from 0 to 7 of sqrt(25-3x) ?
The integral from 0 to 7 of sqrt(25-3x) is 26