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

$$\int_{ -2 }^{ 0 } - { x }^{ 2 } -1 d x$$

Baholash

$$-\frac{14}{3}\approx -4,666666667$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int -x^{2}-1\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int -x^{2}\mathrm{d}x+\int -1\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$-\int x^{2}\mathrm{d}x+\int -1\mathrm{d}x$$

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. -1 ni \frac{x^{3}}{3} marotabaga ko'paytirish.

$$-\frac{x^{3}}{3}+\int -1\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -1 integralini toping.

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

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

$$-\frac{0^{3}}{3}-0-\left(-\frac{\left(-2\right)^{3}}{3}-\left(-2\right)\right)$$

Qisqartirish.

$$-\frac{14}{3}$$