Whakaoti i te f ( x ) = ∫ (from 0 to x) of (t^2-t)dt

$$f ( x ) = \int _ { 0 } ^ { x } ( t ^ { 2 } - t ) d t$$

Aromātai

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

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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

$$\frac{t^{3}}{3}-\int t\mathrm{d}t$$

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

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

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.

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

Whakarūnātia.

$$-\frac{x^{2}}{2}+\frac{x^{3}}{3}$$

Kimi Pārōnaki e ai ki x

$$x\left(x-1\right)$$