integral from 1 to 5 of 5x^2-x/3

Lösung

\int_{1}^{5} 5 x^{2} - \frac{x}{3} d x

\frac{608}{3}

Dezimale

202.66666 \dots

Schritte zur Lösung

\int_{1}^{5} 5 x^{2} - \frac{x}{3} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{5} 5 x^{2} d x - \int_{1}^{5} \frac{x}{3} d x

\int_{1}^{5} 5 x^{2} d x = \frac{620}{3}

\int_{1}^{5} \frac{x}{3} d x = 4

= \frac{620}{3} - 4

Vereinfache

\frac{620}{3} - 4 : \frac{608}{3}

= \frac{608}{3}

\int_{2}^{5} \frac{1}{x - 7} d x

\int_{1}^{4} (4 x^{3} - 3 x^{2} + 1) d x

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

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

\int_{0}^{1} x^{5} (1 - x^{2})^{\frac{3}{2}} d x