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Beliebt Rechnen >

integral from 1 to cos(x) of 10t^9

Lösung

\int_{1}^{c o s (x)} 10 t^{9} d t

Lösung

cos^{10} (x) - 1

Schritte zur Lösung

\int_{1}^{c o s (x)} 10 t^{9} d t

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 10 \cdot \int_{1}^{c o s (x)} t^{9} d t

Wende die Potenzregel an

= 10 [\frac{t ^{10}}{10}]_{1}^{c o s (x)}

Berechne die Grenzen:

\frac{cos ^{10} ( x )}{10} - \frac{1}{10}

= 10 (\frac{cos ^{10} ( x )}{10} - \frac{1}{10})

Vereinfache

= cos^{10} (x) - 1

Beliebte Beispiele

integral from pi/2 to pi of sec^3(x)

\int_{\frac{π}{2}}^{π} sec^{3} (x) d x

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\int_{- 3}^{6} ∣ x - 4 ∣ d x

integral from-1 to 2 of 4x^4

\int_{- 1}^{2} 4 x^{4} d x

integral from 1 to e^8 of ((ln(x))^2)/x

\int_{1}^{e^{8}} \frac{( ln ( x ) ) ^{2}}{x} d x

integral from 0 to 6 of 2x^2

\int_{0}^{6} 2 x^{2} d x