integral from 1-y to e^y of y

Lösung

\int_{1 - y}^{e^{y}} y d y

\frac{e ^{2 y} - 1 + 2 y - y ^{2}}{2}

Schritte zur Lösung

\int_{1 - y}^{e^{y}} y d y

Wende die Potenzregel an

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

Berechne die Grenzen:

\frac{1}{2} e^{2 y} - \frac{( 1 - y ) ^{2}}{2}

= \frac{1}{2} e^{2 y} - \frac{( 1 - y ) ^{2}}{2}

Vereinfache

= \frac{e ^{2 y} - 1 + 2 y - y ^{2}}{2}

\int_{1}^{2} \frac{7}{6} d x

\int_{- \infty}^{0} \frac{1}{( 5 ) ^{3}} d x

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

\int_{0}^{\infty} \frac{2}{1 + t ^{2}} d t

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