What is the integral from 0 to 12 of 2/(sqrt(x+4)) ?

The integral from 0 to 12 of 2/(sqrt(x+4)) is 8

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integral from 0 to 12 of 2/(sqrt(x+4))

\int_{0}^{12} \frac{2}{x + 4} d x

8

Solution steps

\int_{0}^{12} \frac{2}{x + 4} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{12} \frac{1}{x + 4} d x

Apply u-substitution

: \int_{2}^{4} 2 d u

= 2 \cdot \int_{2}^{4} 2 d u

Integral of a constant:

\int a d x = a x

= 2 [2 u]_{2}^{4}

Compute the boundaries:

4

= 2 \cdot 4

Simplify

= 8

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What is the integral from 0 to 12 of 2/(sqrt(x+4)) ?
The integral from 0 to 12 of 2/(sqrt(x+4)) is 8