Whakaoti i te ∫ (from 1 to 8) of (1/sqrt[3]{x}-3x^15) wrt x

$$\int _ { 1 } ^ { 8 } ( \frac { 1 } { \sqrt[ 3 ] { x } } - 3 x ^ { 15 } ) d x$$

Aromātai

$$-\frac{844424930131893}{16}=-5.277655813 \cdot 10^{13}$$

Ngā Upane Otinga

Aromātaitia te tau tōpū tautuhi-kore i te tuatahi.

$$\int \frac{1}{\sqrt[3]{x}}-3x^{15}\mathrm{d}x$$

Kōmitimititia te kīanga tapeke mā te kīanga.

$$\int \frac{1}{\sqrt[3]{x}}\mathrm{d}x+\int -3x^{15}\mathrm{d}x$$

Whakatauwehea te pūmau i ēnei kīanga katoa.

$$\int \frac{1}{\sqrt[3]{x}}\mathrm{d}x-3\int x^{15}\mathrm{d}x$$

Tuhia anō te \frac{1}{\sqrt[3]{x}} hei x^{-\frac{1}{3}}. 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}{3}}\mathrm{d}x ki te \frac{x^{\frac{2}{3}}}{\frac{2}{3}}. Whakarūnātia.

$$\frac{3x^{\frac{2}{3}}}{2}-3\int x^{15}\mathrm{d}x$$

Nā te mea \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} mō te k\neq -1, me whakakapi \int x^{15}\mathrm{d}x ki te \frac{x^{16}}{16}. Whakareatia -3 ki te \frac{x^{16}}{16}.

$$\frac{3x^{\frac{2}{3}}}{2}-\frac{3x^{16}}{16}$$

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.

$$\frac{3}{2}\times 8^{\frac{2}{3}}-\frac{3}{16}\times 8^{16}-\left(\frac{3}{2}\times 1^{\frac{2}{3}}-\frac{3}{16}\times 1^{16}\right)$$

Whakarūnātia.

$$-\frac{844424930131893}{16}$$