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

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

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

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

22

Decimal Notation

2.82842 \dots

Solution steps

\int_{0}^{2} \frac{1}{2 - 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

\int (sin (x))^{- 1} d x

- x, x - x^{2}, 0, 2

\int \frac{x ^{3}}{1} + x^{4} d x

\int cos (n \cdot x) d x

n = 1 \sum \infty \frac{1}{( 2 n + 1 ) ^{3}}

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