What is the integral from 1 to 3 of 1/(sqrt(3-x)) ?

The integral from 1 to 3 of 1/(sqrt(3-x)) is 2sqrt(2)

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integral from 1 to 3 of 1/(sqrt(3-x))

\int_{1}^{3} \frac{1}{3 - x} d x

22

Decimal Notation

2.82842 \dots

Solution steps

\int_{1}^{3} \frac{1}{3 - x} d x

Apply u-substitution

: \int_{2}^{0} - \frac{1}{u} d u

= \int_{2}^{0} - \frac{1}{u} d u

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

= - \int_{0}^{2} - \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}^{2} \frac{1}{u} d u)

Apply the Power Rule

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

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

Simplify

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

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

Compute the boundaries:

22

= 22

(sin (6 x))^{4}

\int_{1}^{e} x^{3} ln (x) d x

\frac{d}{d x} (\frac{x}{20})

y = 7 e^{x} + x, (0, 7)

4

What is the integral from 1 to 3 of 1/(sqrt(3-x)) ?
The integral from 1 to 3 of 1/(sqrt(3-x)) is 2sqrt(2)