What is the integral from 0 to 5 of (56)/(sqrt(x+2)) ?

The integral from 0 to 5 of (56)/(sqrt(x+2)) is 56(2sqrt(7)-2sqrt(2))

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integral from 0 to 5 of (56)/(sqrt(x+2))

\int_{0}^{5} \frac{56}{x + 2} d x

56 (27 - 22)

Decimal

137.93222 \dots

Solution steps

\int_{0}^{5} \frac{56}{x + 2} d x

Take the constant out:

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

= 56 \cdot \int_{0}^{5} \frac{1}{x + 2} d x

Apply u-substitution

: \int_{2}^{7} 2 d u

= 56 \cdot \int_{2}^{7} 2 d u

Integral of a constant:

\int a d x = a x

= 56 [2 u]_{2}^{7}

Compute the boundaries:

27 - 22

= 56 (27 - 22)

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What is the integral from 0 to 5 of (56)/(sqrt(x+2)) ?
The integral from 0 to 5 of (56)/(sqrt(x+2)) is 56(2sqrt(7)-2sqrt(2))