What is the integral from-45 to 0 of 1/(sqrt(4-x)) ?

The integral from-45 to 0 of 1/(sqrt(4-x)) is 10

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integral from-45 to 0 of 1/(sqrt(4-x))

\int_{- 45}^{0} \frac{1}{4 - x} d x

10

Solution steps

\int_{- 45}^{0} \frac{1}{4 - x} d x

Apply u-substitution

= \int_{49}^{4} - \frac{1}{u} d u

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

= - \int_{4}^{49} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{4}^{49} \frac{1}{u} d u)

Apply the Power Rule

= - (- [2 u^{\frac{1}{2}}]_{4}^{49})

Simplify

- (- [2 u^{\frac{1}{2}}]_{4}^{49}) : [2 u]_{4}^{49}

= [2 u]_{4}^{49}

Compute the boundaries:

10

= 10

What is the integral from-45 to 0 of 1/(sqrt(4-x)) ?
The integral from-45 to 0 of 1/(sqrt(4-x)) is 10