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

The integral from 0 to 2 of 2/(sqrt(2-x)) is 4sqrt(2)

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integral from 0 to 2 of 2/(sqrt(2-x))

\int_{0}^{2} \frac{2}{2 - x} d x

42

Decimal

5.65685 \dots

Solution steps

\int_{0}^{2} \frac{2}{2 - x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply u-substitution

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

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

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

= 2 (- \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

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

Apply the Power Rule

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

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

Simplify

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

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

Compute the boundaries:

22

= 2 \cdot 22

Simplify

= 42

\int_{0}^{1} e^{- 8 x} d x

x \to \infty lim \frac{( e ^{\frac{15}{x}} - 1 )}{\frac{15}{x}}

(s + \frac{3}{2})^{2}

\int e^{\frac{- x}{k}} \cdot \frac{- x}{k} d x

x \to \infty lim (x^{3} - 2 x)

What is the integral from 0 to 2 of 2/(sqrt(2-x)) ?
The integral from 0 to 2 of 2/(sqrt(2-x)) is 4sqrt(2)