Ex 7.11, 6 - By using the properties of definite integrals, Evaluate the integrals [x - 5] dx - Ex 7.11

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  1. Chapter 7 Class 12 Integrals
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Ex 7.11, 6 By using the properties of definite integrals, evaluate the integrals: 2﷮8﷮ 𝑥−5﷯﷯𝑑𝑥 𝑥−5﷯= 𝑥−5, 𝑖𝑓 𝑥−5≥0﷮− 𝑥−5﷯ 𝑖𝑓 𝑥−5<0﷯﷯ = 𝑥−5﷯ 𝑖𝑓 𝑥≥5﷮− 𝑥−5﷯ 𝑖𝑓 𝑥<5﷯﷯ ∴ 2﷮8﷮ 𝑥−5﷯﷯𝑑𝑥= 2﷮5﷮− 𝑥−5﷯﷯𝑑𝑥+ 5﷮8﷮ 𝑥−5﷯﷯𝑑𝑥 =− 𝑥﷮2﷯﷮2﷯−5𝑥﷯﷮2﷮5﷯+ 𝑥﷮2﷯﷮2﷯−5𝑥﷯﷮5﷮8﷯ =− 5﷮2﷯﷮2﷯−5×5﷯+ 2﷮2﷯﷮2﷯−5×2﷯+ 8﷮2﷯﷮2﷯−5×8﷯− 5﷮2﷯﷮2﷯−5×5﷯ =− 25﷮2﷯+25+2−10+32−40− 25﷮2﷯+25 =− 25﷮2﷯−25+25−10−40+32+2 = −50﷮2﷯+50−50+34 = −50﷮2﷯+34 = 18﷮2﷯ = 9

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