What is the integral from 0 to 3 of 2/(sqrt(3-x)) ?

The integral from 0 to 3 of 2/(sqrt(3-x)) is 4sqrt(3)

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integral from 0 to 3 of 2/(sqrt(3-x))

\int_{0}^{3} \frac{2}{3 - x} d x

43

Decimal

6.92820 \dots

Solution steps

\int_{0}^{3} \frac{2}{3 - x} d x

Take the constant out:

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

= 2 \cdot \int_{0}^{3} \frac{1}{3 - x} d x

Apply u-substitution

= 2 \cdot \int_{3}^{0} - \frac{1}{u} d u

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

= 2 (- \int_{0}^{3} - \frac{1}{u} d u)

Take the constant out:

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

= 2 (- (- \int_{0}^{3} \frac{1}{u} d u))

Apply the Power Rule

= 2 (- (- [2 u^{\frac{1}{2}}]_{0}^{3}))

Simplify

2 (- (- [2 u^{\frac{1}{2}}]_{0}^{3})) : 2 [2 u]_{0}^{3}

= 2 [2 u]_{0}^{3}

Compute the boundaries:

23

= 2 \cdot 23

Simplify

= 43

What is the integral from 0 to 3 of 2/(sqrt(3-x)) ?
The integral from 0 to 3 of 2/(sqrt(3-x)) is 4sqrt(3)