What is the integral from-7 to 8 of 1/(sqrt(8-x)) ?

The integral from-7 to 8 of 1/(sqrt(8-x)) is 2sqrt(15)

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integral from-7 to 8 of 1/(sqrt(8-x))

\int_{- 7}^{8} \frac{1}{8 - x} d x

215

Decimal

7.74596 \dots

Solution steps

\int_{- 7}^{8} \frac{1}{8 - x} d x

Apply u-substitution

: \int_{15}^{0} - \frac{1}{u} d u

= \int_{15}^{0} - \frac{1}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{15} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{0}^{15} \frac{1}{u} d u)

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{15}

= - (- [2 u^{\frac{1}{2}}]_{0}^{15})

Simplify

- (- [2 u^{\frac{1}{2}}]_{0}^{15}) : [2 u]_{0}^{15}

= [2 u]_{0}^{15}

Compute the boundaries:

215

= 215

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What is the integral from-7 to 8 of 1/(sqrt(8-x)) ?
The integral from-7 to 8 of 1/(sqrt(8-x)) is 2sqrt(15)