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

Lösung

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

\frac{π}{2}

Dezimale

1.57079 \dots

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{3} + 1}{1 + x ^{2}} : \frac{x ^{3}}{1 + x ^{2}} + \frac{1}{1 + x ^{2}}

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

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

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

= 0 + \frac{π}{2}

Vereinfache

= \frac{π}{2}

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