What is the integral from 1 to 3 of 1/(sqrt(x-1)) ?

The integral from 1 to 3 of 1/(sqrt(x-1)) is 2sqrt(2)

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integral from 1 to 3 of 1/(sqrt(x-1))

\int_{1}^{3} \frac{1}{x - 1} d x

22

Decimal

2.82842 \dots

Solution steps

\int_{1}^{3} \frac{1}{x - 1} d x

Apply u-substitution

: \int_{0}^{2} 2 d u

= \int_{0}^{2} 2 d u

Integral of a constant:

\int a d x = a x

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

Compute the boundaries:

22

= 22

\int_{0}^{2} sin^{2} (x) d x

\int_{0}^{1} u d u

\int_{0}^{3} \frac{1}{1 + 1 + x} d x

\int_{- 1}^{2} (x) d x

\int_{- 1}^{4} (2 x - 3) (x - 3) d x

What is the integral from 1 to 3 of 1/(sqrt(x-1)) ?
The integral from 1 to 3 of 1/(sqrt(x-1)) is 2sqrt(2)