Whakaoti i te ∫ (from - 1.5 to 5) of -3x^2+11x+25 wrt x

$$\int _ { - 1.5 } ^ { 5 } - 3 x ^ { 2 } + 11 x + 25 d x$$

Aromātai

$$159.25$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int -3x^{2}+11x+25\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int -3x^{2}\mathrm{d}x+\int 11x\mathrm{d}x+\int 25\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$-3\int x^{2}\mathrm{d}x+11\int x\mathrm{d}x+\int 25\mathrm{d}x$$

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

$$-x^{3}+11\int x\mathrm{d}x+\int 25\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia 11 ki te \frac{x^{2}}{2}.

$$-x^{3}+\frac{11x^{2}}{2}+\int 25\mathrm{d}x$$

Kimihia te tau tōpū o 25 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}x=ax.

$$-x^{3}+\frac{11x^{2}}{2}+25x$$

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.

$$-5^{3}+\frac{11}{2}\times 5^{2}+25\times 5-\left(-\left(-1.5\right)^{3}+\frac{11}{2}\left(-1.5\right)^{2}+25\left(-1.5\right)\right)$$

Whakarūnātia.

$$\frac{637}{4}$$