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

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

Popular >

integral from 0 to 3 of 1/(sqrt(3-x))

\int_{0}^{3} \frac{1}{3 - x} d x

23

Decimal Notation

3.46410 \dots

Solution steps

\int_{0}^{3} \frac{1}{3 - x} d x

Apply u-substitution

: \int_{3}^{0} - \frac{1}{u} d u

= \int_{3}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{3} - \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}^{3} \frac{1}{u} d u)

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{3}

= - (- [2 u^{\frac{1}{2}}]_{0}^{3})

Simplify

- (- [2 u^{\frac{1}{2}}]_{0}^{3}) : [2 u]_{0}^{3}

= [2 u]_{0}^{3}

Compute the boundaries:

23

= 23

\int \frac{1}{2 1 - x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- 2 t}

x - 1, 0

x \to 0 lim (\frac{2}{3 + 4 ^{\frac{1}{0}}})

y = \frac{16 x}{x ^{2} + 16}, (- 2, - \frac{8}{5})

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