What is the integral from-2 to 3 of (33)/(sqrt(3-x)) ?

The integral from-2 to 3 of (33)/(sqrt(3-x)) is 66sqrt(5)

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integral from-2 to 3 of (33)/(sqrt(3-x))

\int_{- 2}^{3} \frac{33}{3 - x} d x

665

Decimal Notation

147.58048 \dots

Solution steps

\int_{- 2}^{3} \frac{33}{3 - x} d x

Take the constant out:

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

= 33 \cdot \int_{- 2}^{3} \frac{1}{3 - x} d x

Apply u-substitution

: \int_{5}^{0} - \frac{1}{u} d u

= 33 \cdot \int_{5}^{0} - \frac{1}{u} d u

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

= 33 (- \int_{0}^{5} - \frac{1}{u} d u)

Take the constant out:

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

= 33 (- (- \int_{0}^{5} \frac{1}{u} d u))

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{5}

= 33 (- (- [2 u^{\frac{1}{2}}]_{0}^{5}))

Simplify

33 (- (- [2 u^{\frac{1}{2}}]_{0}^{5})) : 33 [2 u]_{0}^{5}

= 33 [2 u]_{0}^{5}

Compute the boundaries:

25

= 33 \cdot 25

Simplify

= 665

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What is the integral from-2 to 3 of (33)/(sqrt(3-x)) ?
The integral from-2 to 3 of (33)/(sqrt(3-x)) is 66sqrt(5)