integral from 1 to a of 1/(3t^3)

Lösung

\int_{1}^{a} \frac{1}{3 t ^{3}} d t

\frac{1}{3} (- \frac{1}{2 a ^{2}} + \frac{1}{2})

Schritte zur Lösung

\int_{1}^{a} \frac{1}{3 t ^{3}} d t

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{1}^{a} \frac{1}{t ^{3}} d t

Wende die Potenzregel an

= \frac{1}{3} [- \frac{1}{2 t ^{2}}]_{1}^{a}

Berechne die Grenzen:

- \frac{1}{2 a ^{2}} + \frac{1}{2}

= \frac{1}{3} (- \frac{1}{2 a ^{2}} + \frac{1}{2})

\int_{0}^{π} cos (x) \cdot sin (x) d x

\int_{- 2}^{0} \frac{2}{x ^{2} + 4 x + 8} d x

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

\int_{1}^{3} e^{x} \cdot ln (x) d x

\int_{1}^{4} \frac{1}{( x - 2 ) ^{2}} d x