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

The integral from 1 to 3 of 2/(sqrt(x-1)) is 4sqrt(2)

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

\int_{1}^{3} \frac{2}{x - 1} d x

42

Decimal

5.65685 \dots

Solution steps

\int_{1}^{3} \frac{2}{x - 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{1}^{3} \frac{1}{x - 1} d x

Apply u-substitution

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

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

Integral of a constant:

\int a d x = a x

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

Compute the boundaries:

22

= 2 \cdot 22

Simplify

= 42

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What is the integral from 1 to 3 of 2/(sqrt(x-1)) ?
The integral from 1 to 3 of 2/(sqrt(x-1)) is 4sqrt(2)