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

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

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

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

2

Solution steps

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

Apply u-substitution

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

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

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

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

Apply the Power Rule

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

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

Simplify

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

= [2 u]_{0}^{1}

Compute the boundaries:

2

= 2

\int \frac{1 + cos ( x )}{sin ( x )} d x

x \to 2 lim (\frac{3}{x + 1})

\int (2 x - 5)^{- \frac{1}{2}} d x

\frac{\partial}{\partial x} (y x^{3})

f (x) = \frac{x ^{3} + 7}{x}

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