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

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

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

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

22 - 2

Decimal

0.82842 \dots

Solution steps

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

Apply u-substitution

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

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

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

Apply the Power Rule

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

Simplify

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

= [2 u]_{1}^{2}

Compute the boundaries:

22 - 2

= 22 - 2

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