What is the integral from 0 to 25 of 7/(sqrt(25-x)) ?

The integral from 0 to 25 of 7/(sqrt(25-x)) is 70

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integral from 0 to 25 of 7/(sqrt(25-x))

\int_{0}^{25} \frac{7}{25 - x} d x

70

Solution steps

\int_{0}^{25} \frac{7}{25 - x} d x

Take the constant out:

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

= 7 \cdot \int_{0}^{25} \frac{1}{25 - x} d x

Apply u-substitution

: \int_{25}^{0} - \frac{1}{u} d u

= 7 \cdot \int_{25}^{0} - \frac{1}{u} d u

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

= 7 (- \int_{0}^{25} - \frac{1}{u} d u)

Take the constant out:

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

= 7 (- (- \int_{0}^{25} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{25}

= 7 (- (- [2 u^{\frac{1}{2}}]_{0}^{25}))

Simplify

7 (- (- [2 u^{\frac{1}{2}}]_{0}^{25})) : 7 [2 u]_{0}^{25}

= 7 [2 u]_{0}^{25}

Compute the boundaries:

10

= 7 \cdot 10

Simplify

= 70

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What is the integral from 0 to 25 of 7/(sqrt(25-x)) ?
The integral from 0 to 25 of 7/(sqrt(25-x)) is 70