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Definite Integration by properties - P4
Ex 7.10, 2
Ex 7.10, 3 Important
Example 32 Important
Ex 7.10, 4
Ex 7.10, 15
Ex 7.10, 17
Ex 7.10, 21 (MCQ) Important
Ex 7.10, 19
Ex 7.10, 12 Important
Ex 7.10, 9 You are here
Ex 7.10,7 Important
Example 30
Question 4 (MCQ) Important Deleted for CBSE Board 2024 Exams
Ex 7.10, 10 Important
Ex 7.10,8 Important
Example 34 Important
Ex 7.10, 16 Important
Question 2 Important Deleted for CBSE Board 2024 Exams
Example 42 Important
Definite Integration by properties - P4
Last updated at June 13, 2023 by Teachoo
Ex 7.10, 9 By using the properties of definite integrals, evaluate the integrals : โซ_0^2โ๐ฅโกโ(2โ๐ฅ) ๐๐ฅ Let I=โซ_0^2โใ๐ฅโ(2โ๐ฅ) ๐๐ฅใ โด I=โซ_0^2โใ(2โ๐ฅ) โ(2โ(2โ๐ฅ) ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) โ(2โ2+๐ฅ ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) โ(๐ฅ ) ๐๐ฅใ I=โซ_0^2โใ(2โ๐ฅ) (๐ฅ)^(1/2) ๐๐ฅใ I=โซ_0^2โใ(2. ๐ฅ^(1/2)โ๐ฅ.ใ ๐ฅใ^(1/2) ) ๐๐ฅใ I=2โซ_0^2โใ๐ฅ^(1/2) ๐๐ฅใ โโซ_0^2โใ๐ฅ. ๐ฅ^(3/2) ๐๐ฅใ I=2[๐ฅ^(1/2 + 1)/(1/2 + 1)]_0^2โ [๐ฅ^(3/2 + 1)/(3/2 + 1)]_0^2 I=2[๐ฅ^(3/2 )/(3/2)]_0^2โ [๐ฅ^(5/2)/(5/2)]_0^2 I=(2. 2)/3 [๐ฅ^(3/2) ]_0^2โ ใ2/5 [๐ฅ^(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 [(โ2)^3 ] โ 2/5 [(โ2)^5 ] I=4/3 [2โ2] โ 2/5 [4โ2] I=(8โ2)/3โ(8โ2)/5 I=8โ2 [1/3โ1/5] I=8โ2 [2/15] ๐=(๐๐โ๐)/๐๐