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Beliebt Rechnen >

integral from 0 to 1 of sqrt(9t^4+4t^2)

Lösung

\int_{0}^{1} 9 t^{4} + 4 t^{2} d t

Lösung

\frac{13 13 - 8}{27}

+1

Dezimale

1.43970 \dots

Schritte zur Lösung

\int_{0}^{1} 9 t^{4} + 4 t^{2} d t

Faktorisiere

9 t^{4} + 4 t^{2} : t^{2} 9 t^{2} + 4

= \int_{0}^{1} t^{2} 9 t^{2} + 4 d t

t^{2} = (t),

angenommen

t \geq 0

= \int_{0}^{1} t 9 t^{2} + 4 d t

Wende U-Substitution an

= \int_{4}^{13} \frac{u}{18} d u

Entferne die Konstante:

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

= \frac{1}{18} \cdot \int_{4}^{13} u d u

Wende die Potenzregel an

= \frac{1}{18} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{13}

Berechne die Grenzen:

\frac{26 13}{3} - \frac{16}{3}

= \frac{1}{18} (\frac{26 13}{3} - \frac{16}{3})

Vereinfache

= \frac{13 13 - 8}{27}

Graph

Beliebte Beispiele

integral from 1 to 4 of (x^2+x)

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

derivative of-x^{-2}

\frac{d}{d x} (- x^{- 2})

integral of sqrt(e^x-1)

\int e^{x} - 1 d x

derivative of x^4-8x^2

\frac{d}{d x} (x^{4} - 8 x^{2})

integral from 1 to e^3 of (ln^4(x^2))/x

\int_{1}^{e^{3}} \frac{ln ^{4} ( x ^{2} )}{x} d x