Whakaoti i te ∫ (from -1 to 2) of x^3-x^2 wrt x

$$\int_{ -1 }^{ 2 } { x }^{ 3 } - { x }^{ 2 } d x$$

Aromātai

$$\frac{3}{4}=0.75$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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}.

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

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 -1 ki te \frac{x^{3}}{3}.

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

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.

$$\frac{2^{4}}{4}-\frac{2^{3}}{3}-\left(\frac{\left(-1\right)^{4}}{4}-\frac{\left(-1\right)^{3}}{3}\right)$$

Whakarūnātia.

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