Whakaoti i te a ^ - 1 ( 2 ) = 1,000 e ^ - ∫ (from 0 to 2) of ( 0.03+0.02r)dr

$$a ^ { - 1 } ( 2 ) = 1,000 e ^ { - \int _ { 0 } ^ { 2 } ( 0.03 + 0.02 r ) d r }$$

Whakaoti mō a

$$a=\frac{\sqrt[10]{e}}{500}\approx 0.002210342$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakaraupapatia anō ngā kīanga tau.

$$2\times \frac{1}{a}=1000e^{-\int _{0}^{2}0.02r+0.03\mathrm{d}r}$$

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te a.

$$2\times 1=1000e^{-\int _{0}^{2}0.02r+0.03\mathrm{d}r}a$$

Whakareatia te 2 ki te 1, ka 2.

$$2=1000e^{-\int _{0}^{2}0.02r+0.03\mathrm{d}r}a$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$1000e^{-\int _{0}^{2}0.02r+0.03\mathrm{d}r}a=2$$

He hanga arowhānui tō te whārite.

$$\frac{1000}{\sqrt[10]{e}}a=2$$

Whakawehea ngā taha e rua ki te 1000e^{-\frac{1}{10}}.

$$\frac{\frac{1000}{\sqrt[10]{e}}a\sqrt[10]{e}}{1000}=\frac{2\sqrt[10]{e}}{1000}$$

Mā te whakawehe ki te 1000e^{-\frac{1}{10}} ka wetekia te whakareanga ki te 1000e^{-\frac{1}{10}}.

$$a=\frac{2\sqrt[10]{e}}{1000}$$

Whakawehe 2 ki te 1000e^{-\frac{1}{10}}.

$$a=\frac{\sqrt[10]{e}}{500}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=\frac{\sqrt[10]{e}}{500}\text{, }a\neq 0$$