Whakaoti i te ∫ (from 1 to 2) of (1/sqrt{x}-x) wrt x

$$\int _ { 1 } ^ { 2 } ( \frac { 1 } { \sqrt { x } } - x ) d x$$

Aromātai

$$2\sqrt{2}-\frac{7}{2}\approx -0.671572875$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{1}{\sqrt{x}}-x\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{1}{\sqrt{x}}\mathrm{d}x+\int -x\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int \frac{1}{\sqrt{x}}\mathrm{d}x-\int x\mathrm{d}x$$

Tuhia anō te \frac{1}{\sqrt{x}} hei x^{-\frac{1}{2}}. Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{-\frac{1}{2}}\mathrm{d}x ki te \frac{x^{\frac{1}{2}}}{\frac{1}{2}}. Whakarūnāhia me te tahuri mai i te āhua taupū ki te āhua pūtake.

$$2\sqrt{x}-\int x\mathrm{d}x$$

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 -1 ki te \frac{x^{2}}{2}.

$$2\sqrt{x}-\frac{x^{2}}{2}$$

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.

$$2\times 2^{\frac{1}{2}}-\frac{2^{2}}{2}-\left(2\times 1^{\frac{1}{2}}-\frac{1^{2}}{2}\right)$$

Whakarūnātia.

$$2\sqrt{2}-\frac{7}{2}$$