Whakaoti i te ∫ (from - 2 to 2) of (-0.5x^2+2) wrt x

$$\int _ { - 2 } ^ { 2 } ( - 0.5 x ^ { 2 } + 2 ) d x$$

Aromātai

$$\frac{16}{3}\approx 5.333333333$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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 -0.5 ki te \frac{x^{3}}{3}.

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

Kimihia te tau tōpū o 2 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-\frac{x^{3}}{6}+2x$$

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.

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

Whakarūnātia.

$$\frac{16}{3}$$