Whakaoti i te ∫ (from 0 to 2 cos x) of r-r^2dr

$$\int _ { 0 } ^ { 2 \cos x } r - r ^ { 2 } d r$$

Aromātai

$$\frac{2\left(-4\cos(x)+3\right)\left(\cos(x)\right)^{2}}{3}$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int r-r^{2}\mathrm{d}r$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int r\mathrm{d}r+\int -r^{2}\mathrm{d}r$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int r\mathrm{d}r-\int r^{2}\mathrm{d}r$$

Nā te mea \int r^{k}\mathrm{d}r=\frac{r^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int r\mathrm{d}r ki te \frac{r^{2}}{2}.

$$\frac{r^{2}}{2}-\int r^{2}\mathrm{d}r$$

Nā te mea \int r^{k}\mathrm{d}r=\frac{r^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int r^{2}\mathrm{d}r ki te \frac{r^{3}}{3}. Whakareatia -1 ki te \frac{r^{3}}{3}.

$$\frac{r^{2}}{2}-\frac{r^{3}}{3}$$

Ko te tau tōpū tautuhi ko te pārōnaki kōaro o te kīanga i aromātaitia i te tepe tōrunga o te pāwhaitua, tangohia te pārōnaki kōaro i aromātaitia i te tepe tōraro o te pāwhaitua.

$$\frac{1}{2}\times \left(2\cos(x)\right)^{2}-\frac{1}{3}\times \left(2\cos(x)\right)^{3}-\left(\frac{0^{2}}{2}-\frac{0^{3}}{3}\right)$$

Whakarūnātia.

$$\left(\cos(x)\right)^{2}\left(2-\frac{8\cos(x)}{3}\right)$$

Kimi Pārōnaki e ai ki x

$$2\sin(2x)\left(2\cos(x)-1\right)$$