What is the integral from 2 to 3 of (11)/(sqrt(3-x)) ?

The integral from 2 to 3 of (11)/(sqrt(3-x)) is 22

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integral from 2 to 3 of (11)/(sqrt(3-x))

\int_{2}^{3} \frac{11}{3 - x} d x

22

Solution steps

\int_{2}^{3} \frac{11}{3 - x} d x

Take the constant out:

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

= 11 \cdot \int_{2}^{3} \frac{1}{3 - x} d x

Apply u-substitution

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

= 11 \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

= 11 (- \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

= 11 (- (- \int_{0}^{1} \frac{1}{u} d u))

Apply the Power Rule

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

= 11 (- (- [2 u^{\frac{1}{2}}]_{0}^{1}))

Simplify

11 (- (- [2 u^{\frac{1}{2}}]_{0}^{1})) : 11 [2 u]_{0}^{1}

= 11 [2 u]_{0}^{1}

Compute the boundaries:

2

= 11 \cdot 2

Simplify

= 22

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\frac{d}{d x} (\frac{1}{x} - \frac{1}{sin ( x )})

\frac{d y}{d x} = \frac{6 x ^{4} e ^{\frac{y}{x}} + x ^{2} y ^{2}}{x ^{3} y}

x \to 0 + lim (- x)

\int sec (x) tan (x) - 6 e^{x} d x

What is the integral from 2 to 3 of (11)/(sqrt(3-x)) ?
The integral from 2 to 3 of (11)/(sqrt(3-x)) is 22