integral from 0 to 1 of y(e^y-1)

Lösung

\int_{0}^{1} y (e^{y} - 1) d y

\frac{1}{2}

Dezimale

0.5

Schritte zur Lösung

\int_{0}^{1} y (e^{y} - 1) d y

Wende die partielle Integration an

= [y (e^{y} - y) - \int e^{y} - y d y]_{0}^{1}

\int e^{y} - y d y = e^{y} - \frac{y ^{2}}{2}

= [y (e^{y} - y) - (e^{y} - \frac{y ^{2}}{2})]_{0}^{1}

Vereinfache

[y (e^{y} - y) - (e^{y} - \frac{y ^{2}}{2})]_{0}^{1} : [\frac{1}{2} (- y^{2} + 2 e^{y} y - 2 e^{y})]_{0}^{1}

= [\frac{1}{2} (- y^{2} + 2 e^{y} y - 2 e^{y})]_{0}^{1}

Berechne die Grenzen:

\frac{1}{2}

= \frac{1}{2}

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

\int_{0}^{1} (x^{2} + 4) d x

\int_{0}^{1} sin (n \cdot π \cdot x) d x

\int_{1}^{2} 20 x^{3} + \frac{6}{x ^{2}} d x

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