Whakaoti i te ∫ (from 0 to 11) of 62.5left(11-yright)10 wrt y

$$\int_{ 0 }^{ 11 } 62.5 \left( 11-y \right) 10 d y$$

Aromātai

$$37812.5$$

Ngā Upane Otinga

Whakareatia te 62.5 ki te 10, ka 625.

$$\int _{0}^{11}625\left(11-y\right)\mathrm{d}y$$

Whakamahia te āhuatanga tohatoha hei whakarea te 625 ki te 11-y.

$$\int _{0}^{11}6875-625y\mathrm{d}y$$

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int 6875-625y\mathrm{d}y$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int 6875\mathrm{d}y+\int -625y\mathrm{d}y$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int 6875\mathrm{d}y-625\int y\mathrm{d}y$$

Kimihia te tau tōpū o 6875 mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}y=ay.

$$6875y-625\int y\mathrm{d}y$$

Nā te mea \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int y\mathrm{d}y ki te \frac{y^{2}}{2}. Whakareatia -625 ki te \frac{y^{2}}{2}.

$$6875y-\frac{625y^{2}}{2}$$

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.

$$6875\times 11-\frac{625}{2}\times 11^{2}-\left(6875\times 0-\frac{625}{2}\times 0^{2}\right)$$

Whakarūnātia.

$$\frac{75625}{2}$$