integral from 1 to 2 of (x^3+2)/(x^2)

Lösung

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

\frac{5}{2}

Dezimale

2.5

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{3} + 2}{x ^{2}} : x + \frac{2}{x ^{2}}

= \int_{1}^{2} x + \frac{2}{x ^{2}} 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}^{2} x d x + \int_{1}^{2} \frac{2}{x ^{2}} d x

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

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

= \frac{3}{2} + 1

Vereinfache

\frac{3}{2} + 1 : \frac{5}{2}

= \frac{5}{2}

\int_{2}^{5} (2 x - 3)^{4} d x

\int_{0}^{2} (6 x - 6) (8 x^{2} + 4) d x

\int_{0}^{\frac{π}{2}} π (cos (x))^{2} d x

\int_{1}^{4} 4 x d x

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