Ex 7.11, 9 - Using properties of definite integrals x root 2-x - Ex 7.11

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  1. Chapter 7 Class 12 Integrals
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Ex 7.11, 9 By using the properties of definite integrals, evaluate the integrals : 0﷮2﷮ 𝑥﷮ ﷮2−𝑥﷯﷯﷯ 𝑑𝑥 Let I= 0﷮2﷮𝑥 ﷮2−𝑥﷯ 𝑑𝑥﷯ ∴ I= 0﷮2﷮ 2−𝑥﷯ ﷮2− 2−𝑥﷯ ﷯ 𝑑𝑥﷯ I= 0﷮2﷮ 2−𝑥﷯ ﷮2−2+𝑥 ﷯ 𝑑𝑥﷯ I= 0﷮2﷮ 2−𝑥﷯ ﷮𝑥 ﷯ 𝑑𝑥﷯ I= 0﷮2﷮ 2−𝑥﷯ 𝑥﷯﷮ 1﷮2﷯﷯ 𝑑𝑥﷯ I= 0﷮2﷮ 2. 𝑥﷮ 1﷮2﷯﷯−𝑥. 𝑥﷮ 1﷮2﷯﷯﷯ 𝑑𝑥﷯ I=2 0﷮2﷮ 𝑥﷮ 1﷮2﷯﷯ 𝑑𝑥﷯ − 0﷮2﷮𝑥. 𝑥﷮ 3﷮2﷯﷯ 𝑑𝑥﷯ I=2 𝑥﷮ 1﷮2﷯ + 1﷯﷮ 1﷮2﷯ + 1﷯﷯﷮0﷮2﷯− 𝑥﷮ 3﷮2﷯ + 1﷯﷮ 3﷮2﷯ + 1﷯﷯﷮0﷮2﷯ I=2 𝑥﷮ 3﷮2﷯ ﷯﷮ 3﷮2﷯﷯﷯﷮0﷮2﷯− 𝑥﷮ 5﷮2﷯﷯﷮ 5﷮2﷯﷯﷯﷮0﷮2﷯ I= 2. 2﷮3﷯ 𝑥﷮ 3﷮2﷯﷯﷯﷮0﷮2﷯− 2﷮5﷯ 𝑥﷮ 5﷮2﷯﷯﷯﷮0﷮2﷯ I= 4﷮3﷯ 2﷯﷮ 3﷮2﷯﷯− 0﷯﷮ 3﷮2﷯﷯﷯ − 2﷮5﷯ 2﷯﷮ 5﷮2﷯﷯− 0﷯﷮ 5﷮2﷯﷯﷯ I= 4﷮3﷯ 2﷯﷮ 3﷮2﷯﷯﷯ − 2﷮5﷯ 2﷯﷮ 5﷮2﷯﷯﷯ I= 4﷮3﷯ 2﷯﷮ 1﷮2﷯﷯﷯﷮3﷯﷯ − 2﷮5﷯ 2﷯﷮ 1﷮2﷯﷯﷯﷮3﷯﷯ I= 4﷮3﷯ ﷮2﷯﷯﷮3﷯﷯ − 2﷮5﷯ ﷮2﷯﷯﷮5﷯﷯ I= 4﷮3﷯ 2 ﷮2﷯﷯ − 2﷮5﷯ 4 ﷮2﷯﷯ I= 8 ﷮2﷯﷮3﷯− 8 ﷮2﷯﷮5﷯ I=8 ﷮2﷯ 1﷮3﷯− 1﷮5﷯﷯ I=8 ﷮2﷯ 2﷮15﷯﷯ 𝐈= 𝟏𝟔 ﷮𝟐﷯﷮𝟏𝟓﷯

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