∫ (from 0 to pi / 3) of (1-cosθ)^2 eching

$$\int _ { 0 } ^ { \pi / 3 } ( 1 - \cos \theta ) ^ { 2 }$$

Baholash

$$\frac{\pi \left(\cos(\theta )-1\right)^{2}}{3}$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int \left(1-\cos(\theta )\right)^{2}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, \left(1-\cos(\theta )\right)^{2} integralini toping.

$$\left(1-\cos(\theta )\right)^{2}x$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$\frac{1}{3}\left(1-\cos(\theta )\right)^{2}\pi +0\left(1-\cos(\theta )\right)^{2}$$

Qisqartirish.

$$\frac{\left(\cos(\theta )-1\right)^{2}\pi }{3}$$

θ ga nisbatan hosilani topish

$$-\frac{2\pi \sin(\theta )\left(\cos(\theta )-1\right)}{3}$$