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Beliebt Rechnen >

integral from 0 to 1 of (3x+1)^{sqrt(2)}

Lösung

\int_{0}^{1} (3 x + 1)^{2} d x

Lösung

\frac{2 \cdot 4 ^{2 + 1} - 4 ^{2 + 1} - 2 + 1}{3}

+1

Dezimale

3.78480 \dots

Schritte zur Lösung

\int_{0}^{1} (3 x + 1)^{2} d x

Wende U-Substitution an

= \int_{1}^{4} \frac{u ^{2}}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{1}^{4} u^{2} d u

Wende die Potenzregel an

= \frac{1}{3} [(2 - 1) u^{2 + 1}]_{1}^{4}

Berechne die Grenzen:

2 \cdot 4^{2 + 1} - 4^{2 + 1} - 2 + 1

= \frac{1}{3} (2 \cdot 4^{2 + 1} - 4^{2 + 1} - 2 + 1)

Vereinfache

= \frac{2 \cdot 4 ^{2 + 1} - 4 ^{2 + 1} - 2 + 1}{3}

Graph

Beliebte Beispiele

derivative f(x)=sqrt(8x+1)

d er i v a t i v e f (x) = 8 x + 1

inverselaplace (7s+10)/(7s^2+26s+25)

in v erse l a pl a ce \frac{7 s + 10}{7 s ^{2} + 26 s + 25}

f (x) = - tan (x)

derivative y=e^{4x^2}

d er i v a t i v e y = e^{4 x^{2}}

integral from-2 to 3 of (30)/(x^4)

\int_{- 2}^{3} \frac{30}{x ^{4}} d x