∫ (from - 1 to 2) of (x^2-4x-5) wrt x= eching

$$\int _ { - 1 } ^ { 2 } ( x ^ { 2 } - 4 x - 5 ) d x =$$

Baholash

$$-18$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int x^{2}-4x-5\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int x^{2}\mathrm{d}x+\int -4x\mathrm{d}x+\int -5\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int x^{2}\mathrm{d}x-4\int x\mathrm{d}x+\int -5\mathrm{d}x$$

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.

$$\frac{x^{3}}{3}-4\int x\mathrm{d}x+\int -5\mathrm{d}x$$

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

$$\frac{x^{3}}{3}-2x^{2}+\int -5\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, -5 integralini toping.

$$\frac{x^{3}}{3}-2x^{2}-5x$$

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

$$\frac{2^{3}}{3}-2\times 2^{2}-5\times 2-\left(\frac{\left(-1\right)^{3}}{3}-2\left(-1\right)^{2}-5\left(-1\right)\right)$$

Qisqartirish.

$$-18$$