Chapter 7 Class 12 Integrals
Concept wise

Ex 7.10, 18 - Chapter 7 Class 12 Integrals

Last updated at December 16, 2024 by

Ex 7.10, 18 Class 12 - Evaluate definite integral |x - 1| from 0 to 4 - Ex 7.10

part 2 - Ex 7.10, 18 - Ex 7.10 - Serial order wise - Chapter 7 Class 12 Integrals

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Transcript

Ex 7.10, 18 By using the properties of definite integrals, evaluate the integrals : āˆ«_0^4ā–’|š‘„āˆ’1| š‘‘š‘„ |š‘„āˆ’1|= {ā–ˆ( (š‘„āˆ’1) š‘–š‘“ š‘„āˆ’1ā‰„0@āˆ’(š‘„āˆ’1) š‘–š‘“ š‘„āˆ’1<0)ā”¤ = {ā–ˆ((š‘„āˆ’1,) š‘–š‘“ š‘„ā‰„1@āˆ’(š‘„āˆ’1) š‘–š‘“ š‘„<1)ā”¤ āˆ“ āˆ«_0^4ā–’|š‘„āˆ’1|š‘‘š‘„=āˆ«_0^1ā–’|š‘„āˆ’1|š‘‘š‘„+āˆ«_1^4ā–’|š‘„āˆ’1|š‘‘š‘„ =āˆ«_0^1ā–’怖āˆ’(š‘„āˆ’1)š‘‘š‘„+怗 āˆ«_1^4ā–’(š‘„āˆ’1)š‘‘š‘„ =āˆ«_0^1ā–’怖(āˆ’š‘„+1)š‘‘š‘„+怗 āˆ«_1^4ā–’(š‘„āˆ’1)š‘‘š‘„ =āˆ«_0^1ā–’怖āˆ’š‘„ š‘‘š‘„+怗 āˆ«_0^1ā–’怖1. š‘‘š‘„+āˆ«_1^4ā–’怖š‘„ . š‘‘š‘„āˆ’āˆ«_1^4ā–’怖1.š‘‘š‘„怗怗怗 =āˆ’[š‘„^2/2]_0^1+[š‘„]_0^1āˆ’[š‘„^2/2]_1^4āˆ’[š‘„]_1^4 =āˆ’[((1)^2 āˆ’ 0)/2]+[1āˆ’0]+[((4)^2āˆ’(1)^2)/2]āˆ’[4āˆ’1] =āˆ’1/2+1+[(16 āˆ’ 1)/2]āˆ’3 =āˆ’1/2+15/2āˆ’3+1 =(14 )/2āˆ’2= 7 āˆ’ 2 = 5

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