Ex 7.10, 3 - Chapter 7 Class 12 Integrals
Last updated at July 14, 2026 by Teachoo
Definite Integration by properties - P4
Ex 7.10, 1
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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
- 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
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Definite Integration by properties - P4
- Definite Integration by properties - P6
- Definite Integration by properties - P7
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Transcript
Ex 7.10, 3 By using the properties of definite integrals, evaluate the integrals : ∫_0^(𝜋/2)▒(sin^(3/2)𝑥 𝑑𝑥)/(sin^(3/2)𝑥 + cos^(3/2)𝑥 ) Let I=∫_0^(𝜋/2)▒〖(sin^(3/2) 𝑥)/(sin^(3/2) 𝑥 + cos^(3/2)𝑥 ) 𝑑𝑥〗 I= ∫_0^(𝜋/2)▒〖(sin^(3/2) (𝜋/2 − 𝑥))/(sin^(3/2) (𝜋/2 − 𝑥) + cos^(3/2) (𝜋/2 − 𝑥) ) 𝑑𝑥〗 ∴ I= ∫_0^(𝜋/2)▒〖cos^(3/2)𝑥/(cos^(3/2)𝑥 + sin^(3/2)𝑥 ) 𝑑𝑥〗 Adding (1) and (2) i.e. (1) + (2) I+I= sin^(3/2)𝑥/(sin^(3/2)𝑥 + cos^(3/2)𝑥 ) 𝑑𝑥+∫_0^(𝜋/2)▒〖cos^(3/2)𝑥/(cos^(3/2)𝑥 + sin^(3/2)𝑥 ) 𝑑𝑥〗 2I=∫_0^(𝜋/2)▒〖[(sin^(3/2)𝑥 + cos^(3/2)𝑥)/(sin^(3/2)𝑥 + cos^(3/2)𝑥 )] 𝑑𝑥〗 2I= ∫_0^(𝜋/2)▒〖 𝑑𝑥〗 I=1/2 ∫_0^(𝜋/2)▒〖 𝑑𝑥〗 I=1/2 [𝑥]_0^(𝜋/2) I= 1/2 [𝜋/2−0] I= 𝜋/4
