What is the integral from 0 to 1 of 1/(sqrt(4-x)) ?

The integral from 0 to 1 of 1/(sqrt(4-x)) is 4-2sqrt(3)

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integral from 0 to 1 of 1/(sqrt(4-x))

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

4 - 23

Decimal

0.53589 \dots

Solution steps

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

Apply u-substitution

: \int_{4}^{3} - \frac{1}{u} d u

= \int_{4}^{3} - \frac{1}{u} d u

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

= - \int_{3}^{4} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{3}^{4} \frac{1}{u} d u)

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{3}^{4}

= - (- [2 u^{\frac{1}{2}}]_{3}^{4})

Simplify

- (- [2 u^{\frac{1}{2}}]_{3}^{4}) : [2 u]_{3}^{4}

= [2 u]_{3}^{4}

Compute the boundaries:

4 - 23

= 4 - 23

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What is the integral from 0 to 1 of 1/(sqrt(4-x)) ?
The integral from 0 to 1 of 1/(sqrt(4-x)) is 4-2sqrt(3)