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

Lösung

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

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

Dezimale

0.81026 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \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

Entferne die Konstante:

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

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

Wende die Summenregel an:

\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))

Vereinfache

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

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

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