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

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

Enrhifo

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

Camau Ateb

Gwerthuso’r integryn amhenodol yn gyntaf.

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

Canfod integryn \left(1-\cos(\theta )\right)^{2} gan ddefnyddio'r rheol tabl o integrynnau cyffredin \int a\mathrm{d}x=ax.

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

Yr integryn pendant yw integryn amhendant y mynegiant wedi’i werthuso ar lefel uchaf yr integreiddiad llai’r integryn amhendant ar lefel isaf yr integreiddiad.

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

Symleiddio.

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

Gwahaniaethu w.r.t. θ

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