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

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

Popular >

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

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

- 2 1 - t + 2

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Apply radical rule:

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

Compute the boundaries:

2 1 - t - 2

= - (2 1 - t - 2)

Simplify

= - 2 1 - t + 2

\int_{0}^{1} 8 \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

\int_{0}^{30} t^{2} e^{- t} d t

\int_{1}^{\infty} \frac{6}{x ^{6}} d x

\int_{- 2 π}^{4 π} sin (a x) d x

\int_{0}^{12} x 12 - x d x

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