What is the integral from 4 to 5 of 1/(sqrt(5-x)) ?

The integral from 4 to 5 of 1/(sqrt(5-x)) is 2

Popular >

integral from 4 to 5 of 1/(sqrt(5-x))

\int_{4}^{5} \frac{1}{5 - x} d x

2

Solution steps

\int_{4}^{5} \frac{1}{5 - x} d x

Apply u-substitution

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

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

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

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

Apply the Power Rule

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

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

Simplify

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

= [2 u]_{0}^{1}

Compute the boundaries:

2

= 2

\int_{π}^{2 π} \frac{1 + cos ( x )}{x} d x

\int_{\frac{1}{10}}^{\frac{11}{10}} \frac{1}{x} d x

\int_{4}^{5} \frac{1}{( y - 4 ) ^{\frac{1}{3}}} d y

\int_{1}^{4} (e^{3 x} - \frac{1}{x}) d x

\int_{0}^{1} x 7^{x} d x

What is the integral from 4 to 5 of 1/(sqrt(5-x)) ?
The integral from 4 to 5 of 1/(sqrt(5-x)) is 2