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)

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

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

23

Decimal

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_{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})

Simplify

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

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

Compute the boundaries:

23

= 23

\int cos (x) e^{- 3 x} d x

d er i v a t i v e 2 sin (3 x)

\frac{\partial}{\partial x} (\frac{( 4 x - 4 y )}{4 x + 4 y})

\frac{\partial}{\partial x} (tan (8 + 2 x^{2} y^{4} z^{2}))

a re a 4 cos (3 x), 4 sin (6 x), 0, \frac{π}{6}

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)