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Beliebt Rechnen >

integral from 4 to 16 of 1/(1-sqrt(x))

Lösung

\int_{4}^{16} \frac{1}{1 - x} d x

Lösung

2 (- 2 - ln (3))

+1

Dezimale

- 6.19722 \dots

Schritte zur Lösung

\int_{4}^{16} \frac{1}{1 - x} d x

Wende U-Substitution an

= \int_{- 1}^{- 3} - \frac{2 ( - u + 1 )}{u} d u

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

= - \int_{- 3}^{- 1} - \frac{2 ( - u + 1 )}{u} d u

Entferne die Konstante:

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

= - (- 2 \cdot \int_{- 3}^{- 1} \frac{- u + 1}{u} d u)

Multipliziere aus

\frac{- u + 1}{u} : - 1 + \frac{1}{u}

= - (- 2 \cdot \int_{- 3}^{- 1} - 1 + \frac{1}{u} 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}^{- 1} 1 d u + \int_{- 3}^{- 1} \frac{1}{u} d u))

\int_{- 3}^{- 1} 1 d u = 2

\int_{- 3}^{- 1} \frac{1}{u} d u = - ln (3)

= - (- 2 (- 2 - ln (3)))

Vereinfache

= 2 (- 2 - ln (3))

Graph

Beliebte Beispiele

tangent f(x)=4x^2+4x,\at x=-2

t an g e n t f (x) = 4 x^{2} + 4 x, at x = - 2

integral of e^{-1/4 x^2}

\int e^{- \frac{1}{4} x^{2}} d x

derivative of 1-(1-x/(40)^3)

\frac{d}{d x} (1 - (1 - \frac{x}{40})^{3})

(dy)/(dx)= x/(x^2+1)

\frac{d y}{d x} = \frac{x}{x ^{2} + 1}

2xy^'+y=6x,y(4)=14

2 x y^{^{'}} + y = 6 x, y (4) = 14