integral from 0 to 2 of 5tcos(pit)

Lösung

\int_{0}^{2} 5 t cos (π t) d t

0

Schritte zur Lösung

\int_{0}^{2} 5 t cos (π t) d t

Entferne die Konstante:

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

= 5 \cdot \int_{0}^{2} t cos (π t) d t

Wende die partielle Integration an

= 5 [\frac{1}{π} t sin (π t) - \int \frac{1}{π} sin (π t) d t]_{0}^{2}

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

= 5 [\frac{1}{π} t sin (π t) - (- \frac{1}{π ^{2}} cos (π t))]_{0}^{2}

Vereinfache

= 5 [\frac{1}{π} t sin (π t) + \frac{1}{π ^{2}} cos (π t)]_{0}^{2}

Berechne die Grenzen:

0

= 5 \cdot 0

Vereinfache

= 0

\int_{0}^{2} 5 x cos (π x) d x

\int_{1}^{2} 2 - x d x

\int_{0}^{\frac{1}{2}} sin (2 π x) d x

\int_{0}^{\frac{π}{2}} sin^{2} (θ) d θ

\int_{- 1}^{1} x^{5} d x