∫ (from - 3 to 3) of (9-x^2) wrt x eching

$$\int _ { - 3 } ^ { 3 } ( 9 - x ^ { 2 } ) d x$$

Baholash

$$36$$

Yechim qadamlari

Avval noaniq integralni baholang.

$$\int 9-x^{2}\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int 9\mathrm{d}x+\int -x^{2}\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\int 9\mathrm{d}x-\int x^{2}\mathrm{d}x$$

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 9 integralini toping.

$$9x-\int x^{2}\mathrm{d}x$$

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.

$$9x-\frac{x^{3}}{3}$$

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

$$9\times 3-\frac{3^{3}}{3}-\left(9\left(-3\right)-\frac{\left(-3\right)^{3}}{3}\right)$$

Qisqartirish.

$$36$$