Arxitektura

misоl.

_{I } dx



cos⁶ x

integrаlni hisоblаng.

Yechish. Bu yerdа n = 0, m =-6, m + n =- 6 < 0. Quyidagi almashtirishlardan

foydalanamiz: tgx  z ,

cos² x 

1 _,

1  z <sup>2

dx</sup>  dz . Bundаn,

cos² x

I  _ ¹  ^dx  _ (1 z ² ) ² dz  _ (1 2z ²  z ⁴ )dz 

cos ⁴ x cos ² x

 z  ² z ³  ¹ z ⁵  C  tgx  ² tg ³ x  ¹ tg ⁵ x  C.

3 5 3 5

2. 
   _sin nx sin mxdx, _sin nx cos mxdx,
   

_ cos nx cos mxdx

ko’rinishdagi integrallarni hisoblash

Bu integrallar trigоnоmetrik funksiyalаrning ko’pаytmаsini yig’indigа аlmаshtiruvchi quyidagi fоrmulаlаr yordаmidа hisoblanadi:

cos cos   ¹ [cos(   )  cos(   )],

2

sin  cos   ¹ [sin(   )  sin(   )],

2

sin  sin   ¹ [cos(   )  cos(   )].

2

3. misоl.

I  _ sin 3x  cos 2xdx

integrаlni hisоblаng.

Yechish. Integrаl belgisi оstidаgi funksiyani yig’indigа аlmаshtirаmiz:

I  _sin 3x  cos 2xdx = ¹ _ (sin 5x  sin x)dx  C  ¹ cos 5x  ¹ cos x.

2 10 2

1.3.Ba'zi irratsional ifodalarni intеgrallash.

1. Mavzusining pеdagogik tеxnologik xaritasi

1. 
   Fanning umumiy maqsadi: “Oliy matematika” fanini o’zlashtirishdan maqsad talabalarda uning asosiy tushunchalarini bilish hamda ularni amalda qo’llashda ko’nikma, malaka va shaxsiy fazilatlarni shakllantirishdir
   
2. 
   Mavzuning tartibi: №4
   
3. 
   Mavzu nomi: Ba'zi irratsional ifodalarni intеgrallash
   

4. Mavzuga oid o’quv- ilmiy adabiyotlar:

1. 
   Soatov Yo.U. Oliy matеmatika. 1- tom, T.: 1994-496b.
   
2. 
   Soatov Yo.U. Oliy matеmatika. 3- tom, T.: 1996- 640 b.
   
3. 
   Шипачев В.С. Высшая математика. М.: Высш.шк.,1989-479с.
   

5. 
   Ma'ruzaga ajratilgan vaqt: 2 soat
   

6. Amaliy mashg’ulot(laboratoriya)ga ajratilgan vaqt: 2 soat

7. 
   Mavzuning o’quv maqsadi: talabalarda ba'zi irratsional ifodalarni tеgishli almashtirishlar yordamida hisoblashda bilim, ko’nikma, malaka va shaxsiy fazilatlarni shakllantirishdir
   

8. Mavzu tayanch so’z va iboralarining nomi:

_ m₁ m₂ m_{k }

8.1

_ R^ x, x ⁿ¹ , x ⁿ² ,..., x ^nk





^dx





ko’rinishdagi integrallar

_ m₁ m₂ m_{k }

8.2 _ ^

 ^{ax  b}  ⁿ¹

 ^{ax  b}  ⁿ²

 ^{ax  b}  ^{nk }

^{R x, } cx  d ^{ , } cx  d ^

,..., _{ cx  d  }dx

ko’rinishdagi integrallar

 ^{  }



^{  } 



8.3

_ R(x,

ax ²  bx  c )dx

ko’rinishdagi integrallar


_8.4 dx

(x   )

ko’rinishdagi integrallar

9. Tayanch so’z va iboralarning o’quv maqsadi:

_ m₁ m₂ m_{k }

9.1

_ R^ x, x ⁿ¹ , x ⁿ² ,..., x ^nk





^dx





ko’rinishdagi integrallarni hisoblashni o’rganish

_ m₁ m₂ m_{k }

9.2

_ ^  ^{ax  b}  ⁿ¹  ^{ax  b}  ⁿ²  ^{ax  b}  ^{nk }

^{R x, } cx  d <sup>

, </sup> cx  d ^

,..., _{ cx  d }

_dx

ko’rinishdagi integrallarni hisoblashni

 ^



o’rganish

^{    } 



9.3

_ R(x,

ax ²  bx  c )dx

ko’rinishdagi integrallarni hisoblashni o’rganish


_9.4 dx

(x   )

ko’rinishdagi integrallarni hisoblashni o’rganish

10. Tayanch so’z va iboralar o’quv maqsadlarining toifasi:

_ m₁ m₂ m_{k }

10.1

_ R^ x, x ⁿ¹ , x ⁿ² ,..., x ^nk





^dx





ko’rinishdagi integrallarni hisoblash - qo’llash

_ m₁ m₂ m_{k }

10.2 _ ^

 ^{ax  b}  ⁿ¹ _,  ^{ax  b}  ⁿ² _,...,  ^{ax  b}  ^{nk }

ko’rinishdagi integrallarni hisoblash

^R_ ^x,  _{cx  d} 

^ cx  d <sup>

</sup> cx  d ^

_dx

 ^



- qo’llash

^{    } 



10.3

_ R(x,

ax ²  bx  c )dx

ko’rinishdagi integrallarni hisoblash - qo’llash


10.4 ^dx

(x   )

ko’rinishdagi integrallarni hisoblash - qo’llash

11. 
    O’qitish texnologiyalari: muammoli, “Aqliy xujum” usuli
    

12 . Didaktik vositalar: Proеktor, tarqatma matnlar(slaydlar)
_ m₁ m₂ m_{k }

(№1-

_ R^ x, x ⁿ¹ , x ⁿ² ,..., x ^nk





^dx





ko’rinishdagi integrallarni hisoblash,

_ m₁ m₂ m_{k }

№2- _ ^

 ^{ax  b}  ⁿ¹ _,  ^{ax  b}  ⁿ² _,...,  ^{ax  b}  ^{nk }

ko’rinishdagi integrallarni

^R_ ^x,  _{cx  d} 

^ cx  d <sup>

</sup> cx  d ^

_dx

 ^{     } 

 

hisoblash, № 3- _ R(x,

ax ²  bx  c )dx

ko’rinishdagi integrallarni hisoblash ,


_{№ 4-} dx

(x   )

ko’rinishdagi integrallarni hisoblash).