∫ (from - 4 to 3) of (12-x-x^2) wrt x eching

$$\int _ { - 4 } ^ { 3 } ( 12 - x - x ^ { 2 } ) d x$$

Baholash

$$\frac{343}{6}\approx 57,166666667$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 12-x-x^{2}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 12\mathrm{d}x+\int -x\mathrm{d}x+\int -x^{2}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 12\mathrm{d}x-\int x\mathrm{d}x-\int x^{2}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 12 integralini toping.

$$12x-\int x\mathrm{d}x-\int x^{2}\mathrm{d}x$$

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

$$12x-\frac{x^{2}}{2}-\int x^{2}\mathrm{d}x$$

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

$$12x-\frac{x^{2}}{2}-\frac{x^{3}}{3}$$

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

$$12\times 3-\frac{3^{2}}{2}-\frac{3^{3}}{3}-\left(12\left(-4\right)-\frac{\left(-4\right)^{2}}{2}-\frac{\left(-4\right)^{3}}{3}\right)$$

Qisqartirish.

$$\frac{343}{6}$$