What is the integral from 2 to 3 of (15)/(sqrt(3-x)) ?

The integral from 2 to 3 of (15)/(sqrt(3-x)) is 30

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integral from 2 to 3 of (15)/(sqrt(3-x))

\int_{2}^{3} \frac{15}{3 - x} d x

30

Solution steps

\int_{2}^{3} \frac{15}{3 - x} d x

Take the constant out:

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

= 15 \cdot \int_{2}^{3} \frac{1}{3 - x} d x

Apply u-substitution

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

= 15 \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

= 15 (- \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

= 15 (- (- \int_{0}^{1} \frac{1}{u} d u))

Apply the Power Rule

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

= 15 (- (- [2 u^{\frac{1}{2}}]_{0}^{1}))

Simplify

15 (- (- [2 u^{\frac{1}{2}}]_{0}^{1})) : 15 [2 u]_{0}^{1}

= 15 [2 u]_{0}^{1}

Compute the boundaries:

2

= 15 \cdot 2

Simplify

= 30

- x^{2} + y = 1, [2, - 2]

\int (r^{2} + r + 1) e^{r} d r

x \to 1 + lim (\frac{x ^{2} - 8 x + 15}{x - 1})

2 x y d x + (x^{2} + 1) d y = 3 x d x

What is the integral from 2 to 3 of (15)/(sqrt(3-x)) ?
The integral from 2 to 3 of (15)/(sqrt(3-x)) is 30