Whakaoti i te ∫ (from 0 to 4) of (2x^2-525x)(1-0125(x)) wrt x

$$\int_{ 0 }^{ 4 } (2 { x }^{ 2 } -525x)(1-0125(x)) d x$$

Aromātai

$$-\frac{12472}{3}\approx -4157.333333333$$

Ngā Upane Otinga

Whakareatia te 0 ki te 125, ka 0.

$$\int _{0}^{4}\left(2x^{2}-525x\right)\left(1-0x\right)\mathrm{d}x$$

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

$$\int _{0}^{4}\left(2x^{2}-525x\right)\left(1-0\right)\mathrm{d}x$$

Tangohia te 0 i te 1, ka 1.

$$\int _{0}^{4}\left(2x^{2}-525x\right)\times 1\mathrm{d}x$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2x^{2}-525x ki te 1.

$$\int _{0}^{4}2x^{2}-525x\mathrm{d}x$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 2x^{2}-525x\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 2x^{2}\mathrm{d}x+\int -525x\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$2\int x^{2}\mathrm{d}x-525\int x\mathrm{d}x$$

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

$$\frac{2x^{3}}{3}-525\int x\mathrm{d}x$$

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 -525 ki te \frac{x^{2}}{2}.

$$\frac{2x^{3}}{3}-\frac{525x^{2}}{2}$$

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.

$$\frac{2}{3}\times 4^{3}-\frac{525}{2}\times 4^{2}-\left(\frac{2}{3}\times 0^{3}-\frac{525}{2}\times 0^{2}\right)$$

Whakarūnātia.

$$-\frac{12472}{3}$$