Ex 7.10, 5 - Chapter 7 Class 12 Integrals
Last updated at April 16, 2024 by Teachoo
Definite Integration by properties - P2
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
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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 7.10, 5 By using the properties of definite integrals, evaluate the integrals : ∫_(−5)^5▒〖 |𝑥+2| 〗 𝑑𝑥 |𝑥+2|={█((𝑥+2) 𝑖𝑓 𝑥+2≥0@−(𝑥+2) 𝑖𝑓 𝑥+2<0)┤ ={█((𝑥+2) 𝑖𝑓 𝑥≥−,2@−(𝑥+2) 𝑖𝑓 𝑥<−2)┤ ∴ ∫_(−5)^5▒〖|𝑥+2|𝑑𝑥=∫_(−5)^(−2)▒〖|𝑥+2|𝑑𝑥+〗〗 ∫_(−2)^5▒|𝑥+2|𝑑𝑥 =∫_(−5)^(−2)▒〖−(𝑥+2)𝑑𝑥+〗 ∫_(−2)^5▒(𝑥+2)𝑑𝑥 =−∫_(−5)^(−2)▒〖𝑥𝑑𝑥−〗 ∫_(−5)^(−2)▒2𝑑𝑥+∫_(−2)^5▒𝑥𝑑𝑥+∫_(−2)^5▒2𝑑𝑥 =−[𝑥^2/2]_(−5)^(−2)−2[𝑥]_(−5)^(−2)+[𝑥^2/2]_(−2)^5+2[𝑥]_(−2)^5 =−(((−2)^2 − (−5)^2)/2)−2[−2−(−5)]+[((5)^2 − (−2)^2)/2] +2 [5−(−2)] =−((4 − 25)/2)−2[−2+5]+[(25 − 4)/2]+2[5+2] =−((−21)/2)−2[3]+21/2+2[7] =21/2+21/2−6+14 =42/2+8 = 21+8 = 𝟐𝟗
