What is the integral from 2 to 3 of (38)/(sqrt(3-x)) ?

The integral from 2 to 3 of (38)/(sqrt(3-x)) is 76

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integral from 2 to 3 of (38)/(sqrt(3-x))

\int_{2}^{3} \frac{38}{3 - x} d x

76

Solution steps

\int_{2}^{3} \frac{38}{3 - x} d x

Take the constant out:

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

= 38 \cdot \int_{2}^{3} \frac{1}{3 - x} d x

Apply u-substitution

= 38 \cdot \int_{1}^{0} - \frac{1}{u} d u

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

= 38 (- \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

= 38 (- (- \int_{0}^{1} \frac{1}{u} d u))

Apply the Power Rule

= 38 (- (- [2 u^{\frac{1}{2}}]_{0}^{1}))

Simplify

38 (- (- [2 u^{\frac{1}{2}}]_{0}^{1})) : 38 [2 u]_{0}^{1}

= 38 [2 u]_{0}^{1}

Compute the boundaries:

2

= 38 \cdot 2

Simplify

= 76

3 \frac{d y}{d x} = y^{2}

\frac{d}{d x} (5 x^{2} (x + 47))

\int_{0}^{1} 6 x 5^{x} d x

x \to a lim (1)

t an g e n t 2 x^{3} (2.16)

What is the integral from 2 to 3 of (38)/(sqrt(3-x)) ?
The integral from 2 to 3 of (38)/(sqrt(3-x)) is 76