integral from 0 to t of t^2sin(t)

Lösung

\int_{0}^{t} t^{2} sin (t) d t

- t^{2} cos (t) + 2 (t sin (t) + cos (t)) - 2

Schritte zur Lösung

\int_{0}^{t} t^{2} sin (t) d t

Wende die partielle Integration an

= [- t^{2} cos (t) - \int - 2 t cos (t) d t]_{0}^{t}

\int - 2 t cos (t) d t = - 2 (t sin (t) + cos (t))

= [- t^{2} cos (t) - (- 2 (t sin (t) + cos (t)))]_{0}^{t}

Vereinfache

= [- t^{2} cos (t) + 2 (t sin (t) + cos (t))]_{0}^{t}

Berechne die Grenzen:

- t^{2} cos (t) + 2 (t sin (t) + cos (t)) - 2

= - t^{2} cos (t) + 2 (t sin (t) + cos (t)) - 2

\int_{0}^{1} x^{2} \cdot 3 x^{2} d x

\int_{- 7}^{0} (3 + 49 - x^{2}) d x

\int_{0}^{1} \frac{3 x}{( 2 x + 1 ) ^{3}} d x

\int_{- i}^{3 i} sin (t) d t

\int_{1}^{x^{2}} 16 x y^{3} d y