Whakaoti i te ∫ (from 05 to 1) of p^7(1-p)dp

$$\int _ { 05 } ^ { 1 } p ^ { 7 } ( 1 - p ) d p$$

Aromātai

$$\frac{1}{72}\approx 0.013888889$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te p^{7} ki te 1-p.

$$\int _{0\times 5}^{1}p^{7}-p^{8}\mathrm{d}p$$

Whakareatia te 0 ki te 5, ka 0.

$$\int _{0}^{1}p^{7}-p^{8}\mathrm{d}p$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int p^{7}-p^{8}\mathrm{d}p$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int p^{7}\mathrm{d}p+\int -p^{8}\mathrm{d}p$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int p^{7}\mathrm{d}p-\int p^{8}\mathrm{d}p$$

Nā te mea \int p^{k}\mathrm{d}p=\frac{p^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int p^{7}\mathrm{d}p ki te \frac{p^{8}}{8}.

$$\frac{p^{8}}{8}-\int p^{8}\mathrm{d}p$$

Nā te mea \int p^{k}\mathrm{d}p=\frac{p^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int p^{8}\mathrm{d}p ki te \frac{p^{9}}{9}. Whakareatia -1 ki te \frac{p^{9}}{9}.

$$\frac{p^{8}}{8}-\frac{p^{9}}{9}$$

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.

$$\frac{1^{8}}{8}-\frac{1^{9}}{9}-\left(\frac{0^{8}}{8}-\frac{0^{9}}{9}\right)$$

Whakarūnātia.

$$\frac{1}{72}$$