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

The integral from 0 to 1 of 1/(sqrt(x+2)) is 2sqrt(3)-2sqrt(2)

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integral from 0 to 1 of 1/(sqrt(x+2))

\int_{0}^{1} \frac{1}{x + 2} d x

23 - 22

Decimal

0.63567 \dots

Solution steps

\int_{0}^{1} \frac{1}{x + 2} d x

Apply u-substitution

= \int_{2}^{3} 2 d u

Integral of a constant:

\int a d x = a x

= [2 u]_{2}^{3}

Compute the boundaries:

23 - 22

= 23 - 22

What is the integral from 0 to 1 of 1/(sqrt(x+2)) ?
The integral from 0 to 1 of 1/(sqrt(x+2)) is 2sqrt(3)-2sqrt(2)