Ex 7.6, 21 - Chapter 7 Class 12 Integrals
Last updated at August 11, 2026 by Teachoo
Integration by parts
Example 19
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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
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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
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Transcript
Ex 7.6, 21 - Chapter 7 Class 12 Integrals - NCERT Solution Integrate e^2x sin x I = ∫ e^2x sin x dx Using ILATE e^2x -> Exponential sin x -> Trigonometric We know that ∫ f(x) g(x) dx = f(x) ∫ g(x) dx - ∫ (f'(x) ∫ g(x)dx)dx Putting f(x) = e^2x, g(x) = sin x I = sin . 2 I = sin 2 sin 2 I = sin . 2 2 cos . 2 2 I = 1 2 . 2 sin 1 2 cos . 2 Solving I2 = 1 2 cos . 2 I1 = 1 2 cos . 2 = 1 2 cos 2 cos 2 = 1 2 cos . 2 2 ( sin ) . 2 2 = 1 2 2 . cos 2 + 1 2 2 sin = 1 2 2 . cos 2 + 1 2 I + 1 Putting the value of I1 in (1) , we get I = 2 sin I = 2 sin 2 1 2 2 . cos 2 + I 2 + 1 I = 2 2 sin 2 4 cos I 4 1 + I 4 = 2 sin 2 2 . cos 4 5 4 = 2 4 2 sin cos 1 = 4 5 . 2 4 2 sin cos 4 1 5 = +
