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


Last updated at Dec. 20, 2019 by Teachoo
Transcript
Ex 7.11, 5 By using the properties of definite integrals, evaluate the integrals : โซ_(โ5)^5โใ |๐ฅ+2| ใ ๐๐ฅ |๐ฅ+2|={โ((๐ฅ+2) ๐๐ ๐ฅ+2โฅ0@โ(๐ฅ+2) ๐๐ ๐ฅ+2<0)โค ={โ((๐ฅ+2) ๐๐ ๐ฅโฅโ,2@โ(๐ฅ+2) ๐๐ ๐ฅ<โ2)โค โด โซ_(โ5)^5โใ|๐ฅ+2|๐๐ฅ=โซ_(โ5)^(โ2)โใ|๐ฅ+2|๐๐ฅ+ใใ โซ_(โ2)^5โ|๐ฅ+2|๐๐ฅ Using the Property P2 โซ_๐^๐โใ๐(๐ฅ)๐๐ฅ=โซ_๐^๐โใ๐(๐ฅ)๐๐ฅ+โซ_๐^๐โ๐(๐ฅ)๐๐ฅใใ =โซ_(โ5)^(โ2)โใโ(๐ฅ+2)๐๐ฅ+ใ โซ_(โ2)^5โ(๐ฅ+2)๐๐ฅ =โโซ_(โ5)^(โ2)โใ๐ฅ๐๐ฅโใ โซ_(โ5)^(โ2)โ2๐๐ฅ+โซ_(โ2)^5โ๐ฅ๐๐ฅ+โซ_(โ2)^5โ2๐๐ฅ =โ[๐ฅ^2/2]_(โ5)^(โ2)โ2[๐ฅ]_(โ5)^(โ2)+[๐ฅ^2/2]_(โ2)^5+2[๐ฅ]_(โ2)^5 =โ(((โ2)^2 โ (โ5)^2)/2)โ2[โ2โ(โ5)]+[((5)^2 โ (โ2)^2)/2] +2 [5โ(โ2)] =โ((4 โ 25)/2)โ2[โ2+5]+[(25 โ 4)/2]+2[5+2] =โ((โ21)/2)โ2[3]+21/2+2[7] =21/2+21/2โ6+14 =42/2+8 = 21+8 = ๐๐
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