What is the integral from 1 to 2 of y/(sqrt(5-y)) ?

The integral from 1 to 2 of y/(sqrt(5-y)) is 2(-4sqrt(3)+22/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of y/(sqrt(5-y))

\int_{1}^{2} \frac{y}{5 - y} d y

2 (- 43 + \frac{22}{3})

Decimal

0.81026 \dots

Solution steps

\int_{1}^{2} \frac{y}{5 - y} d y

Apply u-substitution

: \int_{2}^{3} - 2 (- u^{2} + 5) d u

= \int_{2}^{3} - 2 (- u^{2} + 5) d u

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

= - \int_{3}^{2} - 2 (- u^{2} + 5) d u

Take the constant out:

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

= - (- 2 \cdot \int_{3}^{2} - u^{2} + 5 d u)

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (- 2 (- \int_{3}^{2} u^{2} d u + \int_{3}^{2} 5 d u))

\int_{3}^{2} u^{2} d u = \frac{8}{3} - 3

\int_{3}^{2} 5 d u = 10 - 53

= - (- 2 (- (\frac{8}{3} - 3) + 10 - 53))

Simplify

- (- 2 (- (\frac{8}{3} - 3) + 10 - 53)) : 2 (- 43 + \frac{22}{3})

= 2 (- 43 + \frac{22}{3})

\int_{0}^{8.6} 6 - 2 x + 6 x^{2} d x

\int_{1}^{8} (\frac{4}{x} - e^{- x}) d x

\int_{0}^{\frac{π}{4}} x (cos (2 x)) d x

\int_{- 2}^{7} cos (x) d x

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

What is the integral from 1 to 2 of y/(sqrt(5-y)) ?
The integral from 1 to 2 of y/(sqrt(5-y)) is 2(-4sqrt(3)+22/3)