integral from (y^2)/(40) to 20 of (40+x)

Lösung

\int_{\frac{y ^{2}}{40}}^{20} (40 + x) d x

1000 - y^{2} - \frac{y ^{4}}{3200}

Schritte zur Lösung

\int_{\frac{y ^{2}}{40}}^{20} 40 + x 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_{\frac{y ^{2}}{40}}^{20} 40 d x + \int_{\frac{y ^{2}}{40}}^{20} x d x

\int_{\frac{y ^{2}}{40}}^{20} 40 d x = 800 - y^{2}

\int_{\frac{y ^{2}}{40}}^{20} x d x = 200 - \frac{y ^{4}}{3200}

= 800 - y^{2} + 200 - \frac{y ^{4}}{3200}

Vereinfache

= 1000 - y^{2} - \frac{y ^{4}}{3200}

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