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

Lösung

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

- x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

Schritte zur Lösung

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

Wende die Summenregel an:

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

= \int_{x^{3}}^{1 + x} 2 y d y + \int_{x^{3}}^{1 + x} 3 x d y

\int_{x^{3}}^{1 + x} 2 y d y = (1 + x)^{2} - x^{6}

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

= (1 + x)^{2} - x^{6} + 3 x (1 + x) - 3 x^{4}

Vereinfache

(1 + x)^{2} - x^{6} + 3 x (1 + x) - 3 x^{4} : - x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

= - x^{6} - 3 x^{4} + 4 x^{2} + 5 x + 1

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