Submit Search
Upload
Integrals formula and short questions
โข
Download as DOCX, PDF
โข
0 likes
โข
182 views
K
KarunaGupta1982
Follow
Assignment of integrals till 7.4
Read less
Read more
Education
Report
Share
Report
Share
1 of 2
Download now
Recommended
Class 12 chapter 7
Class 12 chapter 7
KarunaGupta1982
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
ใฒใผใ ็่ซ BASIC ๆผ็ฟ99 -ใชในใฏๅ้ฟ็ใชๅ ฅๆญ่ 2-
ใฒใผใ ็่ซ BASIC ๆผ็ฟ99 -ใชในใฏๅ้ฟ็ใชๅ ฅๆญ่ 2-
ssusere0a682
ย
ejercicios de integrales indefinidas (Analisis matematico )
ejercicios de integrales indefinidas (Analisis matematico )
charx_rex
ย
6_DIVERGENSI revisi [anvek] fixeddd.pptx
6_DIVERGENSI revisi [anvek] fixeddd.pptx
immj03771
ย
SUEC ้ซไธญ Adv Maths (Inequalities).pptx
SUEC ้ซไธญ Adv Maths (Inequalities).pptx
tungwc
ย
Recommended
Class 12 chapter 7
Class 12 chapter 7
KarunaGupta1982
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
Kalkulus tugas
Kalkulus tugas
Mohamad Nur Fauzi
ย
ใฒใผใ ็่ซ BASIC ๆผ็ฟ99 -ใชในใฏๅ้ฟ็ใชๅ ฅๆญ่ 2-
ใฒใผใ ็่ซ BASIC ๆผ็ฟ99 -ใชในใฏๅ้ฟ็ใชๅ ฅๆญ่ 2-
ssusere0a682
ย
ejercicios de integrales indefinidas (Analisis matematico )
ejercicios de integrales indefinidas (Analisis matematico )
charx_rex
ย
6_DIVERGENSI revisi [anvek] fixeddd.pptx
6_DIVERGENSI revisi [anvek] fixeddd.pptx
immj03771
ย
SUEC ้ซไธญ Adv Maths (Inequalities).pptx
SUEC ้ซไธญ Adv Maths (Inequalities).pptx
tungwc
ย
Sample paper class XII MATHEMATICS
Sample paper class XII MATHEMATICS
KarunaGupta1982
ย
Class 11 chapters 9, 10, 11
Class 11 chapters 9, 10, 11
KarunaGupta1982
ย
Class xi worksheet (9,10,11) two levels
Class xi worksheet (9,10,11) two levels
KarunaGupta1982
ย
Class xii probability
Class xii probability
KarunaGupta1982
ย
Assignment of straight lines and conic section
Assignment of straight lines and conic section
KarunaGupta1982
ย
Three dimensional geometry
Three dimensional geometry
KarunaGupta1982
ย
Class xii assignment chapters (1 to 9)
Class xii assignment chapters (1 to 9)
KarunaGupta1982
ย
Mcq exemplar class 12
Mcq exemplar class 12
KarunaGupta1982
ย
Mcq exemplar class 12
Mcq exemplar class 12
KarunaGupta1982
ย
Application of integrals
Application of integrals
KarunaGupta1982
ย
Assignment chapters 3 to 7
Assignment chapters 3 to 7
KarunaGupta1982
ย
Surface chemistry notes
Surface chemistry notes
KarunaGupta1982
ย
Assignment of solution
Assignment of solution
KarunaGupta1982
ย
Class X1 assignment of chapters 1,3,4,5
Class X1 assignment of chapters 1,3,4,5
KarunaGupta1982
ย
Continuity and differentiability
Continuity and differentiability
KarunaGupta1982
ย
Notes of Matrices and Determinants
Notes of Matrices and Determinants
KarunaGupta1982
ย
Class xii worksheet (chapters 2,5,6)
Class xii worksheet (chapters 2,5,6)
KarunaGupta1982
ย
Three dimensional geometry
Three dimensional geometry
KarunaGupta1982
ย
Differential equation
Differential equation
KarunaGupta1982
ย
Maxima and minima
Maxima and minima
KarunaGupta1982
ย
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
้ปๅฎข ๆฅๅใTG/ๅพฎไฟกqoqoqdqdใ
ย
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
jakepaige317
ย
More Related Content
More from KarunaGupta1982
Sample paper class XII MATHEMATICS
Sample paper class XII MATHEMATICS
KarunaGupta1982
ย
Class 11 chapters 9, 10, 11
Class 11 chapters 9, 10, 11
KarunaGupta1982
ย
Class xi worksheet (9,10,11) two levels
Class xi worksheet (9,10,11) two levels
KarunaGupta1982
ย
Class xii probability
Class xii probability
KarunaGupta1982
ย
Assignment of straight lines and conic section
Assignment of straight lines and conic section
KarunaGupta1982
ย
Three dimensional geometry
Three dimensional geometry
KarunaGupta1982
ย
Class xii assignment chapters (1 to 9)
Class xii assignment chapters (1 to 9)
KarunaGupta1982
ย
Mcq exemplar class 12
Mcq exemplar class 12
KarunaGupta1982
ย
Mcq exemplar class 12
Mcq exemplar class 12
KarunaGupta1982
ย
Application of integrals
Application of integrals
KarunaGupta1982
ย
Assignment chapters 3 to 7
Assignment chapters 3 to 7
KarunaGupta1982
ย
Surface chemistry notes
Surface chemistry notes
KarunaGupta1982
ย
Assignment of solution
Assignment of solution
KarunaGupta1982
ย
Class X1 assignment of chapters 1,3,4,5
Class X1 assignment of chapters 1,3,4,5
KarunaGupta1982
ย
Continuity and differentiability
Continuity and differentiability
KarunaGupta1982
ย
Notes of Matrices and Determinants
Notes of Matrices and Determinants
KarunaGupta1982
ย
Class xii worksheet (chapters 2,5,6)
Class xii worksheet (chapters 2,5,6)
KarunaGupta1982
ย
Three dimensional geometry
Three dimensional geometry
KarunaGupta1982
ย
Differential equation
Differential equation
KarunaGupta1982
ย
Maxima and minima
Maxima and minima
KarunaGupta1982
ย
More from KarunaGupta1982
(20)
Sample paper class XII MATHEMATICS
Sample paper class XII MATHEMATICS
ย
Class 11 chapters 9, 10, 11
Class 11 chapters 9, 10, 11
ย
Class xi worksheet (9,10,11) two levels
Class xi worksheet (9,10,11) two levels
ย
Class xii probability
Class xii probability
ย
Assignment of straight lines and conic section
Assignment of straight lines and conic section
ย
Three dimensional geometry
Three dimensional geometry
ย
Class xii assignment chapters (1 to 9)
Class xii assignment chapters (1 to 9)
ย
Mcq exemplar class 12
Mcq exemplar class 12
ย
Mcq exemplar class 12
Mcq exemplar class 12
ย
Application of integrals
Application of integrals
ย
Assignment chapters 3 to 7
Assignment chapters 3 to 7
ย
Surface chemistry notes
Surface chemistry notes
ย
Assignment of solution
Assignment of solution
ย
Class X1 assignment of chapters 1,3,4,5
Class X1 assignment of chapters 1,3,4,5
ย
Continuity and differentiability
Continuity and differentiability
ย
Notes of Matrices and Determinants
Notes of Matrices and Determinants
ย
Class xii worksheet (chapters 2,5,6)
Class xii worksheet (chapters 2,5,6)
ย
Three dimensional geometry
Three dimensional geometry
ย
Differential equation
Differential equation
ย
Maxima and minima
Maxima and minima
ย
Recently uploaded
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
้ปๅฎข ๆฅๅใTG/ๅพฎไฟกqoqoqdqdใ
ย
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
jakepaige317
ย
educ6506presentationtc3302771-240427173057-06a46de5.pptx
educ6506presentationtc3302771-240427173057-06a46de5.pptx
mekosin001123
ย
EDUC6506_ClassPresentation_TC330277 (1).pptx
EDUC6506_ClassPresentation_TC330277 (1).pptx
mekosin001123
ย
EDUC6506(001)_ClassPresentation_2_TC330277 (1).pptx
EDUC6506(001)_ClassPresentation_2_TC330277 (1).pptx
mekosin001123
ย
ๆณฝๅ ฐๅบ็จ็งๅญฆๅคงๅญฆๆฏไธ่ฏๅถไฝ/ๅฎๅถๅฝๅคๅคงๅญฆๅฝๅ้็ฅไนฆ/่ดญไนฐไธไธชๅ็ๅปบๅฝ็งๆๅคงๅญฆ็กๅฃซๅญฆไฝ่ฏไนฆ
ๆณฝๅ ฐๅบ็จ็งๅญฆๅคงๅญฆๆฏไธ่ฏๅถไฝ/ๅฎๅถๅฝๅคๅคงๅญฆๅฝๅ้็ฅไนฆ/่ดญไนฐไธไธชๅ็ๅปบๅฝ็งๆๅคงๅญฆ็กๅฃซๅญฆไฝ่ฏไนฆ
jakepaige317
ย
Recently uploaded
(6)
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
1.๐โๅ ฅไพตๅคงๅญฆๅ ฅๅญฆ่่ฏไธญๅฟไฟฎๆนๆ็ปฉโๆฅ่ขญ๏ผALEVELๆฟ่ๅคงๆญ็ง๏ผ่ฝปๆพๆๅฎ่่ฏๆ็ปฉ๏ผ ๐ฅไฝ ่ฟๅจไธบๆ ๆณ่ฟๅ ฅๅคงๅญฆๆ็็ณป็ป่็ฆๆผๅ๏ผๆณ็ฅ้ๅฆไฝ้่ฟๆๆฏๆๆฎตๆดๆน...
ย
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
ๅช้ๅฏไปฅ่ดญไนฐๆฅๆฌ็ญๆณขๅญฆ้ขๅคงๅญฆๅญฆไฝ่ฎฐ/ๅไธชๅ็ๆๅญๅฏ่ฎค่ฏๅ/ไปฟๅถๆฅๆฌๅคงๅญฆๆฏไธ่ฏ/ๆๅคงๅฉ่ฏญCELI่ฏไนฆๅฎๅถ
ย
educ6506presentationtc3302771-240427173057-06a46de5.pptx
educ6506presentationtc3302771-240427173057-06a46de5.pptx
ย
EDUC6506_ClassPresentation_TC330277 (1).pptx
EDUC6506_ClassPresentation_TC330277 (1).pptx
ย
EDUC6506(001)_ClassPresentation_2_TC330277 (1).pptx
EDUC6506(001)_ClassPresentation_2_TC330277 (1).pptx
ย
ๆณฝๅ ฐๅบ็จ็งๅญฆๅคงๅญฆๆฏไธ่ฏๅถไฝ/ๅฎๅถๅฝๅคๅคงๅญฆๅฝๅ้็ฅไนฆ/่ดญไนฐไธไธชๅ็ๅปบๅฝ็งๆๅคงๅญฆ็กๅฃซๅญฆไฝ่ฏไนฆ
ๆณฝๅ ฐๅบ็จ็งๅญฆๅคงๅญฆๆฏไธ่ฏๅถไฝ/ๅฎๅถๅฝๅคๅคงๅญฆๅฝๅ้็ฅไนฆ/่ดญไนฐไธไธชๅ็ๅปบๅฝ็งๆๅคงๅญฆ็กๅฃซๅญฆไฝ่ฏไนฆ
ย
Integrals formula and short questions
1.
CHAPTER โ 7 INTEGRALS Basic
Concepts and Formulae : (i) โซ ๐ฅ ๐ ๐๐ฅ = ๐ฅ ๐+1 ๐+1 + ๐ถ (ii) โซ ๐๐ฅ ๐ฅ = ๐๐๐ | ๐ฅ| + ๐ถ (iii) โซ ๐๐ฅ = ๐ฅ + ๐ถ (iv) โซ ๐๐๐ ๐ฅ ๐๐ฅ = ๐ ๐๐ ๐ฅ + ๐ถ (v) โซ ๐ ๐๐๐ฅ ๐๐ฅ = โ๐๐๐ ๐ฅ + ๐ถ (vi) โซ ๐ ๐๐2 ๐ฅ ๐๐ฅ = ๐ก๐๐ ๐ฅ + ๐ถ (vii) โซ ๐๐๐ ๐๐2 ๐ฅ ๐๐ฅ = โ๐๐๐ก ๐ฅ + ๐ถ (viii) โซ ๐ ๐๐ ๐ฅ ๐ก๐๐ ๐ฅ ๐๐ฅ = ๐ ๐๐ ๐ฅ + ๐ถ (ix) โซ ๐๐๐ ๐๐ ๐ฅ ๐๐๐ก ๐ฅ ๐๐ฅ = โ๐๐๐ ๐๐ ๐ฅ + ๐ถ(x) โซ ๐ ๐ฅ ๐๐ฅ = ๐ ๐ฅ + ๐ถ (xi) โซ ๐ ๐ฅ ๐๐ฅ = ๐ ๐ฅ ๐๐๐ ๐ + ๐ถ (xii) (a) โซ 1 โ1โ๐ฅ2 ๐๐ฅ = sinโ1 ๐ฅ + ๐ถ (b) โซ ๐๐ฅ โ๐2โ๐ฅ2 = sinโ1 ( ๐ฅ ๐ ) + ๐ถ (xiii) (a) โซ 1 1+๐ฅ2 ๐๐ฅ = tanโ1 ๐ฅ + ๐ถ (b) โซ 1 ๐2+๐ฅ2 dx = 1 ๐ tanโ1 ( ๐ฅ ๐ ) + ๐ถ (xiv) โซ 1 ๐ฅโ๐ฅ2โ1 ๐๐ฅ = secโ1 ๐ฅ + ๐ถ (xv) โซโ ๐๐ฅ ๐ฅโ๐ฅ2โ1 = cosecโ1 ๐ฅ + ๐ถ 1. More Standard Results : โซ ๐ก๐๐ ๐ฅ ๐๐ฅ = โ๐๐๐ | ๐๐๐ ๐ฅ| + ๐ถ = ๐๐๐ | ๐ ๐๐ ๐ฅ| + ๐ถ, โซ ๐๐๐ก ๐ฅ ๐๐ฅ = ๐๐๐ | ๐ ๐๐ ๐ฅ| + ๐ถ. โซ ๐ ๐๐ ๐ฅ ๐๐ฅ = ๐๐๐ | ๐ ๐๐ ๐ฅ + ๐ก๐๐ ๐ฅ| + ๐ถ = ๐๐๐ |๐ ๐๐ ( ๐ 4 + ๐ฅ 2 )|+ ๐ถ . โซ ๐๐๐ ๐๐ ๐ฅ ๐๐ฅ = ๐๐๐ | ๐๐๐ ๐๐ ๐ฅ โ ๐๐๐ก ๐ฅ| + ๐ถ = ๐๐๐ |๐ก๐๐ ๐ฅ 2 | + ๐ถ 2. Results ofSome Special Integrals : โซ ๐๐ฅ ๐2 + ๐ฅ2 = 1 ๐ tanโ1 ๐ฅ ๐ + ๐ถ โซ ๐๐ฅ ๐ฅ2 โ ๐2 = 1 2๐ log| ๐ฅ โ ๐ ๐ฅ + ๐ | + ๐ถ โซ ๐๐ฅ ๐2 โ ๐ฅ2 = 1 2๐ log| ๐ + ๐ฅ ๐ โ ๐ฅ | + ๐ถ โซ 1 โ๐2+๐ฅ2 ๐๐ฅ = ๐๐๐ | ๐ฅ + โ๐ฅ2 + ๐2| +C โซ 1 โ๐ฅ2โ๐2 ๐๐ฅ = ๐๐๐ | ๐ฅ + โ๐ฅ2 โ ๐2| +C โซ 1 โ๐2 โ ๐ฅ2 ๐๐ฅ = sinโ1 ๐ฅ ๐ + ๐ถ โซโ๐2 โ ๐ฅ2 ๐๐ฅ = ๐ฅ 2 โ๐2 โ ๐ฅ2 + ๐2 2 sinโ1 ๐ฅ ๐ + ๐ถ โซโ๐2 + ๐ฅ2 ๐๐ฅ = ๐ฅ 2 โ๐ฅ2 + ๐2 + ๐2 2 ๐๐๐ | ๐ฅ + โ๐ฅ2 + ๐2| +C โซโ๐ฅ2 โ ๐2 ๐๐ฅ = ๐ฅ 2 โ๐ฅ2 โ ๐2 - ๐2 2 ๐๐๐ | ๐ฅ + โ๐ฅ2 โ ๐2| +C
2.
1. Integrate the
following w.r.t.x. (i)โซ 1 ๐ฅ3 ๐๐ฅ. (ii) โซ 1 โ ๐ฅ dx. (iii) โซ ๐ ๐๐2 ๐ฅ ๐๐๐ ๐๐2 ๐ฅ ๐๐ฅ. (iv) โซ ๐ก๐๐2 ๐ฅ ๐๐ฅ (v) โซ ๐๐๐ก2 ๐ฅ ๐๐ฅ (vi) โซ ๐๐ฅ ๐ ๐๐2 ๐ฅ ๐๐๐ 2 ๐ฅ . (vii) โซ 2 ๐๐๐ ๐ฅ 3๐ ๐๐2 ๐ฅ ๐๐ฅ. (viii) โซ(2 ๐ก๐๐ ๐ฅ โ 3 ๐๐๐ก ๐ฅ)2 ๐๐ฅ. (ix) โซ ๐ฅ3 ๐ ๐๐ ( ๐ฅ4) ๐๐ฅ (x) โซ ๐ ๐๐2( ๐๐๐ ๐ฅ) ๐ฅ dx (xi) โซ ๐ฅ ๐ ๐ฅ2 dx (xii) โซ (1+๐๐๐๐ฅ)2 ๐ฅ dx (xiii) โซ ๐ฅ2 1+๐ฅ3 dx (xiv) โซ ๐ฅ+๐๐๐ 6๐ฅ 3๐ฅ2+ ๐ ๐๐ 6๐ฅ dx (xv) โซ(2๐ฅ + 4)โ๐ฅ2 + 4๐ฅ + 3 dx (xvi) โซ 1+๐ ๐๐2๐ฅ ๐ฅ+๐ ๐๐2 ๐ฅ dx (xvii) โซ 1+๐ก๐๐๐ฅ ๐ฅ+๐๐๐ ๐ ๐๐๐ฅ dx (xviii) โซ ๐๐ฅ ๐ฅ+โ ๐ฅ (xix) โซ ๐๐ฅ 4๐ฅ2โ9 (xx) โซ ๐ฅ3 1+๐ฅ8 dx (xxi) โซ ๐ฅ2+4๐ฅ ๐ฅ3+6๐ฅ2+5 dx (xxii) โซ ๐ ๐๐2 ๐ฅ 3+๐ก๐๐ ๐ฅ dx 2. Evaluate the following: (i)โซ ๐ฅ2+1 ( ๐ฅ+1)2 dx (ii)โซ ๐๐ฅ 1+๐ก๐๐ ๐ฅ (iii)โซ ๐๐ฅ 1+๐๐๐ก ๐ฅ (iv)โซ ๐ ๐๐4 ๐ฅ ๐๐ฅ (v)โซ ๐๐๐ 4 ๐ฅ ๐๐ฅ (vi)โซ ๐๐๐ 2๐ฅ ( ๐๐๐ ๐ฅ+๐ ๐๐ ๐ฅ)2 dx (vii)โซ ๐๐๐ 5 ๐ฅ ๐ ๐๐ ๐ฅ dx (viii)โซ โ ๐ก๐๐ ๐ฅ ๐ ๐๐ ๐ฅ ๐๐๐ ๐ฅ dx (ix)โซ ๐๐ฅ โ๐ ๐๐3 ๐ฅ ๐ ๐๐ (๐ฅ+๐ผ) dx (x)โซ ๐ ๐๐ ๐ฅ ๐ ๐๐ (๐ฅ+๐) dx (xi)โซ ๐๐๐ 2๐ฅโ๐๐๐ ๐ผ ๐๐๐ ๐ฅโ๐๐๐ ๐ผ dx (xii)โซ ๐๐ฅ ๐๐๐ ( ๐ฅโ๐) ๐๐๐ (๐ฅโ๐) (xiii)โซ ๐๐๐ 2๐ฅ ๐๐๐ 4๐ฅ ๐๐๐ 6๐ฅ ๐๐ฅ (xiv)โซ ๐ ๐๐ 2๐ฅ ๐2 ๐ ๐๐2 ๐ฅ+๐2 ๐๐๐ 2 ๐ฅ dx (xv) โซ ๐ฅ+2 2๐ฅ2+6๐ฅ+5 dx (xvi)โซ ๐๐ฅ โ7โ6๐ฅโ๐ฅ2 (xvii)โซ 5๐ฅ+3 โ๐ฅ2+4๐ฅ+10 dx (xviii)โซ ๐ ๐๐( ๐ฅโ ๐ผ ๐ ๐๐ (๐ฅ+ ๐ผ) dx (xix)โซ ๐ฅ ๐ฅ4โ๐ฅ2+1 dx (xx)โซ 2๐ฅ โ1โ๐ฅ2โ๐ฅ4 dx (xxi)โซ ๐ ๐ฅ โ5โ4๐ ๐ฅโ๐2๐ฅ dx (xxii)โซ ๐๐๐ ๐ฅ โ๐ ๐๐2 ๐ฅโ2 ๐ ๐๐ ๐ฅโ3 dx (xxiii)โซ ๐ฅ โ1โ๐ฅ2+๐ฅ4 dx (xxiv)โซ 2๐ฅโ1 ( ๐ฅโ1)( ๐ฅ+2) ๐ฅโ3) dx (xxv)โซ 3๐ฅโ2 ( ๐ฅ+1)2(๐ฅ+3) dx (xxvi)โซ ๐ ๐๐ ๐ฅ (1โ๐๐๐ ๐ฅ)(2โ๐๐๐ ๐ฅ) dx (xxvii)โซ ๐ฅ ( ๐ฅ2+1)(๐ฅ+1) dx (xxviii)โซ ๐๐ฅ ๐ฅ( ๐ฅ5+1) dx (xxix)โซโ ๐ก๐๐ ๐ฅ ๐๐ฅ (xxx)โซ 2๐ฅ ( ๐ฅ2+1)(๐ฅ2+3) dx (xxxi) โซ ๐ฅ2 (1+๐ฅ3)(2+๐ฅ3) dx (xxxii)โซ ๐๐ฅ ๐ฅ[6( ๐๐๐ ๐ฅ)2+7 ๐๐๐ ๐ฅ+2] dx
Download now