Whakaoti i te ∫ (from 1 to 2) of 6(x^2-1)

$$\int _ { 1 } ^ { 2 } 6 ( x ^ { 2 } - 1 )$$

Aromātai

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Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 6 ki te x^{2}-1.

$$\int _{1}^{2}6x^{2}-6\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 6x^{2}-6\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 6x^{2}\mathrm{d}x+\int -6\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$6\int x^{2}\mathrm{d}x+\int -6\mathrm{d}x$$

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

$$2x^{3}+\int -6\mathrm{d}x$$

Kimihia te tau tōpū o -6 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$2x^{3}-6x$$

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.

$$2\times 2^{3}-6\times 2-\left(2\times 1^{3}-6\right)$$

Whakarūnātia.

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