What is the integral from 0 to 8 of 3/(sqrt(8-x)) ?

The integral from 0 to 8 of 3/(sqrt(8-x)) is 12sqrt(2)

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integral from 0 to 8 of 3/(sqrt(8-x))

\int_{0}^{8} \frac{3}{8 - x} d x

122

Decimal Notation

16.97056 \dots

Solution steps

\int_{0}^{8} \frac{3}{8 - x} d x

Take the constant out:

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

= 3 \cdot \int_{0}^{8} \frac{1}{8 - x} d x

Apply u-substitution

: \int_{8}^{0} - \frac{1}{u} d u

= 3 \cdot \int_{8}^{0} - \frac{1}{u} d u

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

= 3 (- \int_{0}^{8} - \frac{1}{u} d u)

Take the constant out:

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

= 3 (- (- \int_{0}^{8} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{8}

= 3 (- (- [2 u^{\frac{1}{2}}]_{0}^{8}))

Simplify

3 (- (- [2 u^{\frac{1}{2}}]_{0}^{8})) : 3 [2 u]_{0}^{8}

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

Compute the boundaries:

42

= 3 \cdot 42

Simplify

= 122

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What is the integral from 0 to 8 of 3/(sqrt(8-x)) ?
The integral from 0 to 8 of 3/(sqrt(8-x)) is 12sqrt(2)