Whakaoti i te ∫ (from - 1 to 1) of (4x^2-3) wrt x

$$\int _ { - 1 } ^ { 1 } ( 4 x ^ { 2 } - 3 ) d x$$

Aromātai

$$-\frac{10}{3}\approx -3.333333333$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 4x^{2}-3\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 4x^{2}\mathrm{d}x+\int -3\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$4\int x^{2}\mathrm{d}x+\int -3\mathrm{d}x$$

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 4 ki te \frac{x^{3}}{3}.

$$\frac{4x^{3}}{3}+\int -3\mathrm{d}x$$

Kimihia te tau tōpū o -3 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

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

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.

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

Whakarūnātia.

$$-\frac{10}{3}$$