What is the integral from 0 to 6 of 4/(sqrt(6-x)) ?

The integral from 0 to 6 of 4/(sqrt(6-x)) is 8sqrt(6)

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integral from 0 to 6 of 4/(sqrt(6-x))

\int_{0}^{6} \frac{4}{6 - x} d x

86

Decimal Notation

19.59591 \dots

Solution steps

\int_{0}^{6} \frac{4}{6 - x} d x

Take the constant out:

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

= 4 \cdot \int_{0}^{6} \frac{1}{6 - x} d x

Apply u-substitution

: \int_{6}^{0} - \frac{1}{u} d u

= 4 \cdot \int_{6}^{0} - \frac{1}{u} d u

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

= 4 (- \int_{0}^{6} - \frac{1}{u} d u)

Take the constant out:

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

= 4 (- (- \int_{0}^{6} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{6}

= 4 (- (- [2 u^{\frac{1}{2}}]_{0}^{6}))

Simplify

4 (- (- [2 u^{\frac{1}{2}}]_{0}^{6})) : 4 [2 u]_{0}^{6}

= 4 [2 u]_{0}^{6}

Compute the boundaries:

26

= 4 \cdot 26

Simplify

= 86

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What is the integral from 0 to 6 of 4/(sqrt(6-x)) ?
The integral from 0 to 6 of 4/(sqrt(6-x)) is 8sqrt(6)