integral from x^2 to sqrt(x of)(x^2+y^2)

Lösung

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

x^{2} x - x^{4} + \frac{x ^{\frac{3}{2}} - x ^{6}}{3}

Schritte zur Lösung

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

\int_{x^{2}}^{x} x^{2} d y = x^{2} x - x^{4}

\int_{x^{2}}^{x} y^{2} d y = \frac{x ^{\frac{3}{2}} - x ^{6}}{3}

= x^{2} x - x^{4} + \frac{x ^{\frac{3}{2}} - x ^{6}}{3}

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