integral from 0 to 2 of (4t-1)^{10}

Lösung

\int_{0}^{2} (4 t - 1)^{10} d t

\frac{7 ^{11} + 1}{44}

Dezimale

44939244.18181 \dots

Schritte zur Lösung

\int_{0}^{2} (4 t - 1)^{10} d t

Wende U-Substitution an

= \int_{- 1}^{7} \frac{u ^{10}}{4} d u

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int_{- 1}^{7} u^{10} d u

Wende die Potenzregel an

= \frac{1}{4} [\frac{u ^{11}}{11}]_{- 1}^{7}

Berechne die Grenzen:

\frac{7 ^{11}}{11} + \frac{1}{11}

= \frac{1}{4} (\frac{7 ^{11}}{11} + \frac{1}{11})

Vereinfache

= \frac{7 ^{11} + 1}{44}

\int_{3}^{4} (x - 3) (4 - x) d x

\int_{0}^{π} 2 - 2 cos (t) d t

\int_{0}^{2} \frac{x}{1 + 10 x ^{2}} d x

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

\int_{0}^{2} 4 - x d x