Definite Integration by properties - P4

Chapter 7 Class 12 Integrals
Concept wise

### Transcript

Ex 7.10, 9 By using the properties of definite integrals, evaluate the integrals : โซ_0^2โ๐ฅโกโ(2โ๐ฅ) ๐๐ฅ Let I=โซ_0^2โใ๐ฅโ(2โ๐ฅ) ๐๐ฅใ โด I=โซ_0^2โใ(2โ๐ฅ) โ(2โ(2โ๐ฅ) ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) โ(2โ2+๐ฅ ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) โ(๐ฅ ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) (๐ฅ)^(1/2) ๐๐ฅใ I=โซ_0^2โใ(2. ๐ฅ^(1/2)โ๐ฅ.ใ ๐ฅใ^(1/2) ) ๐๐ฅใ I=2โซ_0^2โใ๐ฅ^(1/2) ๐๐ฅใ โโซ_0^2โใ๐ฅ. ๐ฅ^(3/2) ๐๐ฅใ I=2[๐ฅ^(1/2 + 1)/(1/2 + 1)]_0^2โ [๐ฅ^(3/2 + 1)/(3/2 + 1)]_0^2 I=2[๐ฅ^(3/2 )/(3/2)]_0^2โ [๐ฅ^(5/2)/(5/2)]_0^2 I=(2. 2)/3 [๐ฅ^(3/2) ]_0^2โ ใ2/5 [๐ฅ^(5/2) ]ใ_0^2 I=4/3 [(2)^(3/2)โ(0)^(3/2) ] โ 2/5 [(2)^(5/2)โ(0)^(5/2) ] I=4/3 [(2)^(3/2) ] โ 2/5 [(2)^(5/2) ] I=4/3 [[(2)^(1/2) ]^3 ] โ 2/5 [[(2)^(1/2) ]^3 ] I=4/3 [(โ2)^3 ] โ 2/5 [(โ2)^5 ] I=4/3 [2โ2] โ 2/5 [4โ2] I=(8โ2)/3โ(8โ2)/5 I=8โ2 [1/3โ1/5] I=8โ2 [2/15] ๐=(๐๐โ๐)/๐๐