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

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

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

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

- 2 t - 1

Solution steps

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

Apply u-substitution

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

Integral of a constant:

\int a d x = a x

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

Compute the boundaries:

- 2 t - 1

= - 2 t - 1

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