integral from 0 to 2pi of 8tsqrt(2)

Lösung

\int_{0}^{2 π} 8 t 2 d t

162 π^{2}

Dezimale

223.32365 \dots

Schritte zur Lösung

\int_{0}^{2 π} 8 t 2 d t

Entferne die Konstante:

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

= 82 \cdot \int_{0}^{2 π} t d t

Wende die Potenzregel an

= 82 [\frac{t ^{2}}{2}]_{0}^{2 π}

Berechne die Grenzen:

2 π^{2}

= 82 \cdot 2 π^{2}

Vereinfache

= 162 π^{2}

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

\int_{0}^{r} (a r^{3} + b r) 2 π r d r

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

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

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