∫ (from - 1 to 073) of -1/2x^3+3x-2 wrt x eching

$$\int _ { - 1 } ^ { 073 } - \frac { 1 } { 2 } x ^ { 3 } + 3 x - 2 d x$$

Baholash

$$-\frac{27}{8}=-3,375$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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{1}{2} ni \frac{x^{4}}{4} marotabaga ko'paytirish.

$$-\frac{x^{4}}{8}+3\int x\mathrm{d}x+\int -2\mathrm{d}x$$

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. 3 ni \frac{x^{2}}{2} marotabaga ko'paytirish.

$$-\frac{x^{4}}{8}+\frac{3x^{2}}{2}+\int -2\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -2 integralini toping.

$$-\frac{x^{4}}{8}+\frac{3x^{2}}{2}-2x$$

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

$$-\frac{1}{8}\times \left(0\times 73\right)^{4}+\frac{3}{2}\times \left(0\times 73\right)^{2}-2\times 0\times 73-\left(-\frac{\left(-1\right)^{4}}{8}+\frac{3}{2}\left(-1\right)^{2}-2\left(-1\right)\right)$$

Qisqartirish.

$$-\frac{27}{8}$$