What is the integral from 3 to 5 of 1/(sqrt(5-x)) ?

The integral from 3 to 5 of 1/(sqrt(5-x)) is 2sqrt(2)

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integral from 3 to 5 of 1/(sqrt(5-x))

\int_{3}^{5} \frac{1}{5 - x} d x

22

Decimal

2.82842 \dots

Solution steps

\int_{3}^{5} \frac{1}{5 - x} d x

Apply u-substitution

: \int_{2}^{0} - \frac{1}{u} d u

= \int_{2}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{2} - \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}^{2} \frac{1}{u} d u)

Apply the Power Rule

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

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

Simplify

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

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

Compute the boundaries:

22

= 22

\frac{3.49}{x ^{0.432}}

\frac{d}{d x} (\frac{1}{3 ( 1 + x ) ^{\frac{2}{3}}})

f (x) = (e^{3 x} - 1)^{5}

c y^{- 9}

\frac{\partial}{\partial x} (- \frac{1}{r})

What is the integral from 3 to 5 of 1/(sqrt(5-x)) ?
The integral from 3 to 5 of 1/(sqrt(5-x)) is 2sqrt(2)