integral from 1 to 2 of 4/((x-1)^{1/4)}

Lösung

\int_{1}^{2} \frac{4}{( x - 1 ) ^{\frac{1}{4}}} d x

\frac{16}{3}

Dezimale

5.33333 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{4}{( x - 1 ) ^{\frac{1}{4}}} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{2} \frac{1}{( x - 1 ) ^{\frac{1}{4}}} d x

Wende Exponentenregel an:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{( x - 1 ) ^{\frac{1}{4}}} = (x - 1)^{- \frac{1}{4}}

= 4 \cdot \int_{1}^{2} (x - 1)^{- \frac{1}{4}} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{1} \frac{1}{u ^{\frac{1}{4}}} d u

Wende die Potenzregel an

= 4 [\frac{4}{3} u^{\frac{3}{4}}]_{0}^{1}

Berechne die Grenzen:

\frac{4}{3}

= 4 \cdot \frac{4}{3}

Vereinfache

= \frac{16}{3}

x \to 3 + lim (\frac{3 x}{x - 3})

x \to 1 lim (\frac{x ^{m} - 1}{x - 1})

t an g e n t f (x) = \frac{x ^{2}}{x - 3}, at x = 0

y d y = x d x

\frac{d}{d y} (9 - y^{2})