Baholash
\frac{34}{3}\approx 11,333333333
Baham ko'rish
Klipbordga nusxa olish
\int _{0}^{2}3x+2x^{2}\mathrm{d}x
x ga 3+2x ni ko'paytirish orqali distributiv xususiyatdan foydalanish.
\int 3x+2x^{2}\mathrm{d}x
Avval noaniq integralni baholang.
\int 3x\mathrm{d}x+\int 2x^{2}\mathrm{d}x
Summani muddatma-muddat integratsiya qiling.
3\int x\mathrm{d}x+2\int x^{2}\mathrm{d}x
Har bir shartda konstantani qavsdan tashqariga oling.
\frac{3x^{2}}{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\mathrm{d}x integralni \frac{x^{2}}{2} bilan almashtiring. 3 ni \frac{x^{2}}{2} marotabaga ko'paytirish.
\frac{3x^{2}}{2}+\frac{2x^{3}}{3}
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. 2 ni \frac{x^{3}}{3} marotabaga ko'paytirish.
\frac{3}{2}\times 2^{2}+\frac{2}{3}\times 2^{3}-\left(\frac{3}{2}\times 0^{2}+\frac{2}{3}\times 0^{3}\right)
Xos integral bu integral hisoblashning yuqori chegarasida hisoblangan ifodaning boshlangʻich holatidan chiqarib tashlagan holda integral hisoblashning quyi chegarasida hisoblangan ifodaning boshlangʻich holatidir.
\frac{34}{3}
Qisqartirish.
Misollar
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