Integration Full Chapter Explained - Integration Class 12 - Everything you need

Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.11, 18 By using the properties of definite integrals, evaluate the integrals : โซ_0^4โ|๐ฅโ1| ๐๐ฅ |๐ฅโ1|= {โ( (๐ฅโ1) ๐๐ ๐ฅโ1โฅ0@โ(๐ฅโ1) ๐๐ ๐ฅโ1<0)โค = {โ((๐ฅโ1,) ๐๐ ๐ฅโฅ1@โ(๐ฅโ1) ๐๐ ๐ฅ<1)โค โด โซ_0^4โ|๐ฅโ1|๐๐ฅ=โซ_0^1โ|๐ฅโ1|๐๐ฅ+โซ_1^4โ|๐ฅโ1|๐๐ฅ Using the property, P2 P2 :- โซ_๐^๐โใ๐(๐ฅ)๐๐ฅ=ใ โซ_๐^๐โใ๐(๐ฅ)๐๐ฅ+โซ_๐^๐โ๐(๐ฅ)๐๐ฅใ =โซ_0^1โใโ(๐ฅโ1)๐๐ฅ+ใ โซ_1^4โ(๐ฅโ1)๐๐ฅ =โซ_0^1โใ(โ๐ฅ+1)๐๐ฅ+ใ โซ_1^4โ(๐ฅโ1)๐๐ฅ =โซ_0^1โใโ๐ฅ ๐๐ฅ+ใ โซ_0^1โใ1. ๐๐ฅ+โซ_1^4โใ๐ฅ . ๐๐ฅโโซ_1^4โใ1.๐๐ฅใใใ =โ[๐ฅ^2/2]_0^1+[๐ฅ]_0^1โ[๐ฅ^2/2]_1^4โ[๐ฅ]_1^4 =โ[((1)^2 โ 0)/2]+[1โ0]+[((4)^2โ(1)^2)/2]โ[4โ1] =โ1/2+1+[(16 โ 1)/2]โ3 =โ1/2+15/2โ3+1 =(14 )/2โ2= 7 โ 2 = 5
Ex 7.11
Ex 7.11, 2
Ex 7.11, 3
Ex 7.11, 4
Ex 7.11, 5 Important
Ex 7.11, 6
Ex 7.11,7 Important
Ex 7.11,8 Important
Ex 7.11, 9
Ex 7.11, 10 Important
Ex 7.11, 11 Important
Ex 7.11, 12 Important
Ex 7.11, 13
Ex 7.11, 14
Ex 7.11, 15
Ex 7.11, 16
Ex 7.11, 17
Ex 7.11, 18 Important You are here
Ex 7.11, 19
Ex 7.11, 20 Important
Ex 7.11, 21 Important
About the Author