What is the integral from 0 to 4 of 1/(sqrt(4-x)) ?

The integral from 0 to 4 of 1/(sqrt(4-x)) is 4

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integral from 0 to 4 of 1/(sqrt(4-x))

\int_{0}^{4} \frac{1}{4 - x} d x

4

Solution steps

\int_{0}^{4} \frac{1}{4 - 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

\frac{2 x ^{3} + 8}{x}

\frac{2}{1 - x ^{2}}, 0

\int cos (x) cos (x) d x

\frac{\partial}{\partial x} (90 - 4 x^{2} - 1 y^{2})

y^{^{'}} = \frac{t ^{2}}{y} (1 + t^{3})

What is the integral from 0 to 4 of 1/(sqrt(4-x)) ?
The integral from 0 to 4 of 1/(sqrt(4-x)) is 4