Whakaoti i te ∫ (from 2 to 5) of 5/sqrt{x wrt x

$$\int _ { 2 } ^ { 5 } \frac { 5 } { \sqrt { x } } d x$$

Aromātai

$$10\left(\sqrt{5}-\sqrt{2}\right)\approx 8.218544151$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{5}{\sqrt{x}}\mathrm{d}x$$

Whakatauwehetia te pūmau mā te whakamahi i te \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$5\int \frac{1}{\sqrt{x}}\mathrm{d}x$$

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.

$$10\sqrt{x}$$

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.

$$10\times 5^{\frac{1}{2}}-10\times 2^{\frac{1}{2}}$$

Whakarūnātia.

$$10\sqrt{5}-10\sqrt{2}$$