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

The integral from-1 to 4 of 1/(sqrt(4-x)) is 2sqrt(5)

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

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

25

Decimal Notation

4.47213 \dots

Solution steps

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

Apply u-substitution

: \int_{5}^{0} - \frac{1}{u} d u

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

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

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

Take the constant out:

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

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

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{5}

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

Simplify

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

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

Compute the boundaries:

25

= 25

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What is the integral from-1 to 4 of 1/(sqrt(4-x)) ?
The integral from-1 to 4 of 1/(sqrt(4-x)) is 2sqrt(5)