What is the integral from 0 to a of 1/(sqrt(a-x)) ?

The integral from 0 to a of 1/(sqrt(a-x)) is 2sqrt(a)

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integral from 0 to a of 1/(sqrt(a-x))

\int_{0}^{a} \frac{1}{a - x} d x

2 a

Solution steps

\int_{0}^{a} \frac{1}{a - x} d x

Apply u-substitution

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

= \int_{a}^{0} - \frac{1}{u} d u

Take the constant out:

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

= - \int_{a}^{0} \frac{1}{u} d u

Apply the Power Rule

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

= - [2 u^{\frac{1}{2}}]_{a}^{0}

Apply radical rule:

= - [2 u]_{a}^{0}

Compute the boundaries:

- 2 a

= - (- 2 a)

Simplify

= 2 a

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What is the integral from 0 to a of 1/(sqrt(a-x)) ?
The integral from 0 to a of 1/(sqrt(a-x)) is 2sqrt(a)