integral from 0 to pi of cot(x)tan(x)

Lösung

\int_{0}^{π} cot (x) tan (x) d x

π

Dezimale

3.14159 \dots

Schritte zur Lösung

\int_{0}^{π} cot (x) tan (x) d x

Nimm den/die Nenner von

cot (x) tan (x)

und vergleiche mit Null:

x = \frac{π}{2}

Wenn

b, a < b < c, f (b) =

unbestimmt

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{0}^{\frac{π}{2}} cot (x) tan (x) d x + \int_{\frac{π}{2}}^{π} cot (x) tan (x) d x

\int_{0}^{\frac{π}{2}} cot (x) tan (x) d x = \frac{π}{2}

\int_{\frac{π}{2}}^{π} cot (x) tan (x) d x = π - \frac{π}{2}

= \frac{π}{2} + π - \frac{π}{2}

Vereinfache

= π

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

\int_{0}^{\frac{1}{2}} 60 x^{2} (1 - x)^{3} d x

\int_{1}^{5} 2 x + 4 d x

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

\int_{- \infty}^{0} sin (x) e^{x} d x