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Ex 7.1, 15 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Chapter 7 Class 12 Integrals
Concept wise
-
Using Formulaes
- Using Trignometric Formulaes
- Integration by substitution - x^n
- Integration by substitution - lnx
- Integration by substitution - e^x
- Integration by substitution - Trignometric - Normal
- Integration by substitution - Trignometric - Inverse
- Integration using trigo identities - sin^2,cos^2 etc formulae
- Integration using trigo identities - a-b formulae
- Integration using trigo identities - 2x formulae
- Integration using trigo identities - 3x formulae
- Integration using trigo identities - CD and CD inv formulae
- Integration using trigo identities - Inv Trigo formulae
- Integration by parts
- Integration by parts - e^x integration
- Integration by specific formulaes - Formula 1
- Integration by specific formulaes - Formula 2
- Integration by specific formulaes - Formula 3
- Integration by specific formulaes - Formula 4
- Integration by specific formulaes - Formula 5
- Integration by specific formulaes - Formula 6
- Integration by specific formulaes - Formula 7
- Integration by specific formulaes - Formula 8
- Integration by specific formulaes - Method 9
- Integration by specific formulaes - Method 10
- Integration by partial fraction - Type 1
- Integration by partial fraction - Type 2
- Integration by partial fraction - Type 3
- Integration by partial fraction - Type 4
- Integration by partial fraction - Type 5
- Definite Integral as a limit of a sum
- Definite Integration - By Formulae
- Definite Integration - By Partial Fraction
- Definite Integration - By e formula
- Definite Integration - By Substitution
- Definite Integration by properties - P2
- Definite Integration by properties - P3
- Definite Integration by properties - P4
- Definite Integration by properties - P6
- Definite Integration by properties - P7
Transcript
Ex 7.1, 15 𝑥(3 𝑥2+2𝑥+3)𝑑𝑥 𝑥(3 𝑥2+2𝑥+3)𝑑𝑥 = 𝑥 12 3 𝑥2+2𝑥+3𝑑𝑥 = 3 𝑥 12 . 𝑥2+2 𝑥 12 . 𝑥+3 𝑥 12𝑑𝑥 = 3 𝑥 12 + 2+2 𝑥 12 + 1+3 𝑥 12𝑑𝑥 = 3 𝑥 1 + 42+2 𝑥 1 + 22+3 𝑥 12𝑑𝑥 = 3 𝑥 52+2 𝑥 32+3 𝑥 12𝑑𝑥 =3 𝑥 52𝑑𝑥+2 𝑥 32𝑑𝑥+3 𝑥 12𝑑𝑥 = 3 . 𝑥 52 + 1 52 + 1 + 2 . 𝑥 32 + 1 32 + 1 + 3 𝑥 12 + 1 12 + 1+𝐶 = 3𝑥 72 72 + 2 𝑥 52 52 + 3 𝑥 32 32 +𝐶 =3× 2 𝑥 727 +2× 2 𝑥 52 5 +3× 2 𝑥 323 +𝐶 = 𝟔 𝒙 𝟕𝟐𝟕 + 𝟒 𝒙 𝟓𝟐 𝟓 + 𝟐𝒙 𝟑𝟐+𝑪
