Whakaoti i te ∫ (from - 1 to 1) of t(1-2t)dt

$$\int _ { - 1 } ^ { 1 } t ( 1 - 2 t ) d t$$

Aromātai

$$-\frac{4}{3}\approx -1.333333333$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te t ki te 1-2t.

$$\int _{-1}^{1}t-2t^{2}\mathrm{d}t$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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}.

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

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}. Whakareatia -2 ki te \frac{t^{3}}{3}.

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

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.

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

Whakarūnātia.

$$-\frac{4}{3}$$