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

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

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integral from 1 to 5 of 1/(sqrt(5-x))

\int_{1}^{5} \frac{1}{5 - x} d x

4

Solution steps

\int_{1}^{5} \frac{1}{5 - x} d x

Apply u-substitution

: \int_{4}^{0} - \frac{1}{u} d u

= \int_{4}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{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_{0}^{4} \frac{1}{u} d u)

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{4}

= - (- [2 u^{\frac{1}{2}}]_{0}^{4})

Simplify

- (- [2 u^{\frac{1}{2}}]_{0}^{4}) : [2 u]_{0}^{4}

= [2 u]_{0}^{4}

Compute the boundaries:

4

= 4

\int_{- 1}^{3} 3 x^{2} + 5 x - 1 d x

\int_{4}^{5} 5 d x

\int_{0}^{1} 3 x^{2} sin (x^{3}) d x

\int_{0}^{1} x \cdot e^{3 x} d x

\int_{1}^{2} x^{3} e^{x} d x

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