Ex 7.8, 12 - Chapter 7 Class 12 Integrals
Last updated at August 18, 2026 by Teachoo
Definite Integration - By Formulae
Ex 7.8, 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
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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 7.8, 12 ∫_0^(𝜋/2)▒〖𝑐𝑜𝑠2 𝑥 𝑑𝑥〗 Step 1 :- Let F(𝑥)=∫1▒〖𝑐𝑜𝑠^2 𝑥 𝑑𝑥〗 = ∫1▒(cos2𝑥 + 1)/2 𝑑𝑥 =1/2 ∫1▒〖𝑐𝑜𝑠 2𝑥 𝑑𝑥+1/2 ∫1▒𝑑𝑥〗 =1/2 × (𝑠𝑖𝑛 2𝑥)/2+𝑥/2 =1/4 𝑠𝑖𝑛 2𝑥+ 𝑥/2 Hence , F(𝑥)=1/4 𝑠𝑖𝑛 2𝑥+ 𝑥/2 Step 2 :- ∫_0^(𝜋/2)▒〖𝑐𝑜𝑠^2 𝑥=𝐹(𝜋/2)−𝐹(0) 〗 =1/4 𝑠𝑖𝑛(2 ×𝜋/2)+((𝜋/2))/2−1/4 𝑠𝑖𝑛(2×0/2)−0/2 =1/4 𝑠𝑖𝑛(𝜋)+𝜋/4−1/4 〖 sin〗〖0 −0〗 =1/4 ×0+ 𝜋/4− 1/4 ×0−0 = 𝝅/𝟒
