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

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

Aromātai

$$48$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

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

Kōmitimititia te kīanga tapeke mā te kīanga.

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

Whakatauwehea te pūmau i ēnei kīanga katoa.

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

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}.

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

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

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

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.

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

Whakarūnātia.

$$48$$