integral from 0 to cos(θ) of 3r^2

Lösung

\int_{0}^{c o s (θ)} 3 r^{2} d r

cos^{3} (θ)

Schritte zur Lösung

\int_{0}^{c o s (θ)} 3 r^{2} d r

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{c o s (θ)} r^{2} d r

Wende die Potenzregel an

= 3 [\frac{r ^{3}}{3}]_{0}^{c o s (θ)}

Berechne die Grenzen:

\frac{cos ^{3} ( θ )}{3}

= 3 \cdot \frac{cos ^{3} ( θ )}{3}

Vereinfache

= cos^{3} (θ)

\int_{1}^{x} \frac{5 - x}{8} d x

\int_{0}^{1} \frac{1}{5 + 2 x} d x

\int_{- 2}^{0} (20 x - e^{x}) d x

\int_{0}^{1} 4 x^{e} + 3 e^{x} d x

\int_{1}^{3} x x d x