integral from 0 to 1 of 4x^3e^{x^4}

Lösung

\int_{0}^{1} 4 x^{3} e^{x^{4}} d x

e - 1

Dezimale

1.71828 \dots

Schritte zur Lösung

\int_{0}^{1} 4 x^{3} e^{x^{4}} d x

Entferne die Konstante:

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

= 4 \cdot \int_{0}^{1} x^{3} e^{x^{4}} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{1} \frac{e ^{u^{\frac{4}{3}}} u ^{\frac{1}{3}}}{3} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{3} \cdot \int_{0}^{1} e^{u^{\frac{4}{3}}} u^{\frac{1}{3}} d u

Wende U-Substitution an

= 4 \cdot \frac{1}{3} \cdot \int_{0}^{1} \frac{3 e ^{v}}{4} d v

Entferne die Konstante:

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

= 4 \cdot \frac{1}{3} \cdot \frac{3}{4} \cdot \int_{0}^{1} e^{v} d v

Nutze das gemeinsame Integral :

\int e^{v} d v = e^{v}

= 4 \cdot \frac{1}{3} \cdot \frac{3}{4} [e^{v}]_{0}^{1}

Vereinfache

4 \cdot \frac{1}{3} \cdot \frac{3}{4} [e^{v}]_{0}^{1} : [e^{v}]_{0}^{1}

= [e^{v}]_{0}^{1}

Berechne die Grenzen:

e - 1

= e - 1

x 1 - y^{2} d x + y 1 + x^{2} d y = 0

\int_{0}^{1} \frac{1}{x ^{2} - 3} d x

\int \frac{9 x ^{2} + x + 48}{( x + 3 ) ( x ^{2} + 9 )} d x

\frac{\partial}{\partial y} (x y e^{s i n (π x y)})

a re a y = 2, y = sec (x)