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Chapter 7 Class 12 Integrals
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Ex 7.11, 18 Class 12 - Evaluate definite integral |x - 1| from 0 to 4

Ex 7.11, 18 - Chapter 7 Class 12 Integrals - Part 2

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Transcript

Ex 7.11, 18 By using the properties of definite integrals, evaluate the integrals : ∫_0^4▒|𝑥−1| 𝑑𝑥 |𝑥−1|= {█( (𝑥−1) 𝑖𝑓 𝑥−1≥0@−(𝑥−1) 𝑖𝑓 𝑥−1<0)┤ = {█((𝑥−1,) 𝑖𝑓 𝑥≥1@−(𝑥−1) 𝑖𝑓 𝑥<1)┤ ∴ ∫_0^4▒|𝑥−1|𝑑𝑥=∫_0^1▒|𝑥−1|𝑑𝑥+∫_1^4▒|𝑥−1|𝑑𝑥 Using the property, P2 P2 :- ∫_𝑎^𝑏▒〖𝑓(𝑥)𝑑𝑥=〗 ∫_𝑎^𝑐▒〖𝑓(𝑥)𝑑𝑥+∫_𝑐^𝑏▒𝑓(𝑥)𝑑𝑥〗 =∫_0^1▒〖−(𝑥−1)𝑑𝑥+〗 ∫_1^4▒(𝑥−1)𝑑𝑥 =∫_0^1▒〖(−𝑥+1)𝑑𝑥+〗 ∫_1^4▒(𝑥−1)𝑑𝑥 =∫_0^1▒〖−𝑥 𝑑𝑥+〗 ∫_0^1▒〖1. 𝑑𝑥+∫_1^4▒〖𝑥 . 𝑑𝑥−∫_1^4▒〖1.𝑑𝑥〗〗〗 =−[𝑥^2/2]_0^1+[𝑥]_0^1−[𝑥^2/2]_1^4−[𝑥]_1^4 =−[((1)^2 − 0)/2]+[1−0]+[((4)^2−(1)^2)/2]−[4−1] =−1/2+1+[(16 − 1)/2]−3 =−1/2+15/2−3+1 =(14 )/2−2= 7 − 2 = 5

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.