What is the integral from 0 to 10 of 5/(sqrt(10-x)) ?

The integral from 0 to 10 of 5/(sqrt(10-x)) is 10sqrt(10)

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integral from 0 to 10 of 5/(sqrt(10-x))

\int_{0}^{10} \frac{5}{10 - x} d x

1010

Decimal

31.62277 \dots

Solution steps

\int_{0}^{10} \frac{5}{10 - x} d x

Take the constant out:

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

= 5 \cdot \int_{0}^{10} \frac{1}{10 - x} d x

Apply u-substitution

: \int_{10}^{0} - \frac{1}{u} d u

= 5 \cdot \int_{10}^{0} - \frac{1}{u} d u

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

= 5 (- \int_{0}^{10} - \frac{1}{u} d u)

Take the constant out:

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

= 5 (- (- \int_{0}^{10} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{10}

= 5 (- (- [2 u^{\frac{1}{2}}]_{0}^{10}))

Simplify

5 (- (- [2 u^{\frac{1}{2}}]_{0}^{10})) : 5 [2 u]_{0}^{10}

= 5 [2 u]_{0}^{10}

Compute the boundaries:

210

= 5 \cdot 210

Simplify

= 1010

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What is the integral from 0 to 10 of 5/(sqrt(10-x)) ?
The integral from 0 to 10 of 5/(sqrt(10-x)) is 10sqrt(10)