integral from pi/4 to pi/2 of 3cot^3(x)

Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} 3 cot^{3} (x) d x

3 (\frac{1}{2} - \frac{1}{2} ln (2))

Dezimale

0.46027 \dots

Schritte zur Lösung

\int_{\frac{π}{4}}^{\frac{π}{2}} 3 cot^{3} (x) d x

Entferne die Konstante:

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

= 3 \cdot \int_{\frac{π}{4}}^{\frac{π}{2}} cot^{3} (x) d x

Wende integrale Reduktion an

= 3 (- [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x)

\int_{\frac{π}{4}}^{\frac{π}{2}} cot (x) d x = \frac{1}{2} ln (2)

= 3 (- [\frac{cot ^{2} ( x )}{2}]_{\frac{π}{4}}^{\frac{π}{2}} - \frac{1}{2} ln (2))

Berechne die Grenzen:

- \frac{1}{2}

= 3 (- (- \frac{1}{2}) - \frac{1}{2} ln (2))

Vereinfache

= 3 (\frac{1}{2} - \frac{1}{2} ln (2))

\int_{0}^{1} (x^{- 2} + 3 e^{3 x}) d x

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\int_{0}^{1} \frac{x ^{2}}{( 1 + x )} d x

\int_{0}^{l n (2)} e^{- y} d y

\int_{0}^{\frac{π}{2}} cos (k x) d x