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Bu berilgan masala uchun quyidagi aniqlikda integralni hisoblash kerak:

\[
\int_{1}^{2} x^4 \, dx
\]

### Qadam 1: Integrallashtirish
Eng avvalo, $x^4$ funksiyasini integrallaymiz:

\[
\int x^4 \, dx = \frac{x^5}{5} + C
\]

Bu yerda $C$ - doimiy.

### Qadam 2: Chegaralangan integrallash
Chegaralar orasidagi (1 dan 2 gacha) aniq integralni hisoblash uchun, $x = 2$ va $x = 1$ ni joylashtiramiz:

\[
\int_{1}^{2} x^4 \, dx = \left[\frac{x^5}{5}\right]_1^2 = \frac{2^5}{5} - \frac{1^5}{5}
\]

### Qadam 3: Natijani hisoblash
Endi ifodalarni hisoblaymiz:

\[
\frac{2^5}{5} = \frac{32}{5}, \quad \frac{1^5}{5} = \frac{1}{5}
\]

Bu qiymatlarni chiqaramiz:

\[
\frac{32}{5} - \frac{1}{5} = \frac{31}{5} = 6.2
\]

Shunday qilib, aniq integralning qiymati 6.2 ga teng.

Agar sizga qo'shimcha ma'lumot yoki izohlar kerak bo'lsa, ayting. 

### Tegishli Savollar:
1. Integralning umumiy shakli qanday va u qanday hollarda qo'llaniladi?
2. $x^n$ ko'rsatkichli funksiyalarining integrallash qoidalarini tushuntiring.
3. Aniq integral va noaniq integral o'rtasidagi farq nima?
4. Boshqa chegaralar uchun shu integrallash usuli qanday o'zgaradi?
5. Integrallash qoidalari qaysi muammolarni hal qilishda yordam beradi?

### Maslahat:
Doim integrallashdan oldin, funksiyaning cheklangan intervaldagi xususiyatlarini tahlil qiling, chunki bu natijani to'g'ri talqin qilishga yordam beradi.

Learn how to calculate the definite integral ∫_{1}^{2} x^4 dx using detailed step-by-step instructions. This problem involves integral calculus and the power rule for integration. Suitable for advanced high school students and those studying calculus.

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