∫ (from 0 to 5) of (x+2-x/2) wrt x eching

$$\int_{ 0 }^{ 5 } (x+2- \frac{ x }{ 2 } ) d x$$

Baholash

$$\frac{65}{4}=16,25$$

Yechim qadamlari

\frac{1}{2}x ni olish uchun x va -\frac{x}{2} ni birlashtirish.

$$\int _{0}^{5}\frac{1}{2}x+2\mathrm{d}x$$

Avval noaniq integralni baholang.

$$\int \frac{x}{2}+2\mathrm{d}x$$

Summani muddatma-muddat integratsiya qiling.

$$\int \frac{x}{2}\mathrm{d}x+\int 2\mathrm{d}x$$

Har bir shartda konstantani qavsdan tashqariga oling.

$$\frac{\int x\mathrm{d}x}{2}+\int 2\mathrm{d}x$$

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

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

\int a\mathrm{d}x=ax umumiy integrallar qoidasi jadvalidan foydalanib, 2 integralini toping.

$$\frac{x^{2}}{4}+2x$$

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

$$\frac{5^{2}}{4}+2\times 5-\left(\frac{0^{2}}{4}+2\times 0\right)$$

Qisqartirish.

$$\frac{65}{4}$$