Whakaoti i te ∫ (from 1 to 2) of (3t^2-t)dt

$$\int _ { 1 } ^ { 2 } ( 3 t ^ { 2 } - t ) d t$$

Aromātai

$$\frac{11}{2}=5.5$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 3t^{2}-t\mathrm{d}t$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 3t^{2}\mathrm{d}t+\int -t\mathrm{d}t$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$3\int t^{2}\mathrm{d}t-\int t\mathrm{d}t$$

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

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

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}.

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

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.

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

Whakarūnātia.

$$\frac{11}{2}$$