integral from 0 to pi of sin(mx)e^{nx}

Lösung

\int_{0}^{π} sin (m x) e^{n x} d x

\frac{- e ^{πn} m cos ( πm ) + n e ^{πn} sin ( πm ) + m}{m ^{2} + n ^{2}}

Schritte zur Lösung

\int_{0}^{π} sin (m x) e^{n x} d x

Berechne das unbestimmte Integral:

\int sin (m x) e^{n x} d x = - \frac{m e ^{n x} cos ( m x )}{m ^{2} + n ^{2}} + \frac{n e ^{n x} sin ( m x )}{m ^{2} + n ^{2}} + C

Berechne die Grenzen:

\int_{0}^{π} sin (m x) e^{n x} d x = - \frac{m e ^{nπ} cos ( mπ )}{m ^{2} + n ^{2}} + \frac{n e ^{nπ} sin ( mπ )}{m ^{2} + n ^{2}} - (- \frac{m}{m ^{2} + n ^{2}})

= - \frac{m e ^{nπ} cos ( mπ )}{m ^{2} + n ^{2}} + \frac{n e ^{nπ} sin ( mπ )}{m ^{2} + n ^{2}} - (- \frac{m}{m ^{2} + n ^{2}})

Vereinfache

= \frac{- e ^{πn} m cos ( πm ) + n e ^{πn} sin ( πm ) + m}{m ^{2} + n ^{2}}

\int sin (\frac{x π}{2}) d x

\int \frac{( x - 1 ) ^{3}}{x ^{2}} d x

l a pl a ce t r an s f or m g (t) = 4 cos (4 t) - 9 sin (4 t) + 2 cos (10 t)

\frac{\partial}{\partial x} (r sin (t) sin (x))

\frac{\partial}{\partial x} (e^{- (x^{2} + y^{2} + 2 z^{2})})