integral from-1 to 1 of xsin(pix)

Lösung

\int_{- 1}^{1} x sin (π x) d x

\frac{2}{π}

Dezimale

0.63661 \dots

Schritte zur Lösung

\int_{- 1}^{1} x sin (π x) d x

Wende die partielle Integration an

= [- \frac{1}{π} x cos (π x) - \int - \frac{1}{π} cos (π x) d x]_{- 1}^{1}

\int - \frac{1}{π} cos (π x) d x = - \frac{1}{π ^{2}} sin (π x)

= [- \frac{1}{π} x cos (π x) - (- \frac{1}{π ^{2}} sin (π x))]_{- 1}^{1}

Vereinfache

= [- \frac{1}{π} x cos (π x) + \frac{1}{π ^{2}} sin (π x)]_{- 1}^{1}

Berechne die Grenzen:

\frac{2}{π}

= \frac{2}{π}

\int \frac{2}{u} d u

\int_{0}^{1} (1 - x)^{9} d x

d er i v a t i v e f (x) = 7 x + 9

\frac{\partial}{\partial x} ((x^{3} - y^{2})^{2})

\frac{\partial}{\partial x} ((x + y)^{5})