Whakaoti i te ∫ (from 0 to 2) of (24+24x+06x^2)(x) wrt x

$$\int_{ 0 }^{ 2 } (24+24x+06 { x }^{ 2 } )(x) d x$$

Aromātai

$$112$$

Ngā Upane Otinga

Whakareatia te 0 ki te 6, ka 0.

$$\int _{0}^{2}\left(24+24x+0x^{2}\right)x\mathrm{d}x$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$\int _{0}^{2}\left(24+24x+0\right)x\mathrm{d}x$$

Tāpirihia te 24 ki te 0, ka 24.

$$\int _{0}^{2}\left(24+24x\right)x\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24+24x ki te x.

$$\int _{0}^{2}24x+24x^{2}\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 24x+24x^{2}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 24x\mathrm{d}x+\int 24x^{2}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$24\int x\mathrm{d}x+24\int x^{2}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x\mathrm{d}x ki te \frac{x^{2}}{2}. Whakareatia 24 ki te \frac{x^{2}}{2}.

$$12x^{2}+24\int x^{2}\mathrm{d}x$$

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

$$12x^{2}+8x^{3}$$

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.

$$12\times 2^{2}+8\times 2^{3}-\left(12\times 0^{2}+8\times 0^{3}\right)$$

Whakarūnātia.

$$112$$