What is the integral from 100 to 104 of 8sqrt(104-x) ?

The integral from 100 to 104 of 8sqrt(104-x) is 128/3

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integral from 100 to 104 of 8sqrt(104-x)

\int_{100}^{104} 8 104 - x d x

\frac{128}{3}

Decimal

42.66666 \dots

Solution steps

\int_{100}^{104} 8 104 - x d x

Take the constant out:

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

= 8 \cdot \int_{100}^{104} 104 - x d x

Apply u-substitution

: \int_{4}^{0} - u d u

= 8 \cdot \int_{4}^{0} - u d u

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

= 8 (- \int_{0}^{4} - u d u)

Take the constant out:

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

= 8 (- (- \int_{0}^{4} u d u))

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}

= 8 (- (- [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}))

Simplify

= 8 [\frac{2}{3} u^{\frac{3}{2}}]_{0}^{4}

Compute the boundaries:

\frac{16}{3}

= 8 \cdot \frac{16}{3}

Simplify

= \frac{128}{3}

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What is the integral from 100 to 104 of 8sqrt(104-x) ?
The integral from 100 to 104 of 8sqrt(104-x) is 128/3