∫ (from - 1 to 0) of (x^3-2x^2-13x) eching

$$\int _ { - 1 } ^ { 0 } ( x ^ { 3 } - 2 x ^ { 2 } - 13 x )$$

Baholash

$$\frac{67}{12}\approx 5,583333333$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{3}-2x^{2}-13x\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{3}\mathrm{d}x+\int -2x^{2}\mathrm{d}x+\int -13x\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int x^{3}\mathrm{d}x-2\int x^{2}\mathrm{d}x-13\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{3}\mathrm{d}x integralni \frac{x^{4}}{4} bilan almashtiring.

$$\frac{x^{4}}{4}-2\int x^{2}\mathrm{d}x-13\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x^{2}\mathrm{d}x integralni \frac{x^{3}}{3} bilan almashtiring. -2 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$\frac{x^{4}}{4}-\frac{2x^{3}}{3}-13\int x\mathrm{d}x$$

k\neq -1 uchun integral \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} boʻlgani uchun, \int x\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. -13 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$\frac{x^{4}}{4}-\frac{2x^{3}}{3}-\frac{13x^{2}}{2}$$

Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.

$$\frac{0^{4}}{4}-\frac{2}{3}\times 0^{3}-\frac{13}{2}\times 0^{2}-\left(\frac{\left(-1\right)^{4}}{4}-\frac{2}{3}\left(-1\right)^{3}-\frac{13}{2}\left(-1\right)^{2}\right)$$

Qisqartirish.

$$\frac{67}{12}$$