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

$$\int _ { - 3 } ^ { 1 } ( - x ^ { 3 } + 2 x ) d x =$$

Baholash

$$12$$

Yechim qadamlari

Avval noaniq integralni baholang.

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

Summani muddatma-muddat integratsiya qiling.

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

Har bir shartda konstantani qavsdan tashqariga oling.

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

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

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

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

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

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

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

Qisqartirish.

$$12$$