Whakaoti i te ∫ (from 0 to 3) of x^3-2x^2 wrt x

$$\int _ { 0 } ^ { 3 } x ^ { 3 } - 2 x ^ { 2 } d x$$

Aromātai

$$\frac{9}{4}=2.25$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{3}\mathrm{d}x ki te \frac{x^{4}}{4}.

$$\frac{x^{4}}{4}-2\int x^{2}\mathrm{d}x$$

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

$$\frac{x^{4}}{4}-\frac{2x^{3}}{3}$$

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.

$$\frac{3^{4}}{4}-\frac{2}{3}\times 3^{3}-\left(\frac{0^{4}}{4}-\frac{2}{3}\times 0^{3}\right)$$

Whakarūnātia.

$$\frac{9}{4}$$