Chapter 7 Class 12 Integrals
Concept wise

Ex 7.10, 5 - Chapter 7 Class 12 Integrals

Last updated at December 16, 2024 by

Ā  Ex 7.10, 5 - Using properties of definite integrals, |x + 2| dx - Ex 7.10

part 2 - Ex 7.10, 5 - Ex 7.10 - Serial order wise - Chapter 7 Class 12 Integrals
part 3 - Ex 7.10, 5 - Ex 7.10 - Serial order wise - Chapter 7 Class 12 Integrals

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Transcript

Ex 7.10, 5 By using the properties of definite integrals, evaluate the integrals : āˆ«_(āˆ’5)^5ā–’怖 |š‘„+2| 怗 š‘‘š‘„ |š‘„+2|={ā–ˆ((š‘„+2) š‘–š‘“ š‘„+2ā‰„0@āˆ’(š‘„+2) š‘–š‘“ š‘„+2<0)ā”¤ ={ā–ˆ((š‘„+2) š‘–š‘“ š‘„ā‰„āˆ’,2@āˆ’(š‘„+2) š‘–š‘“ š‘„<āˆ’2)ā”¤ āˆ“ āˆ«_(āˆ’5)^5ā–’怖|š‘„+2|š‘‘š‘„=āˆ«_(āˆ’5)^(āˆ’2)ā–’怖|š‘„+2|š‘‘š‘„+怗怗 āˆ«_(āˆ’2)^5ā–’|š‘„+2|š‘‘š‘„ =āˆ«_(āˆ’5)^(āˆ’2)ā–’怖āˆ’(š‘„+2)š‘‘š‘„+怗 āˆ«_(āˆ’2)^5ā–’(š‘„+2)š‘‘š‘„ =āˆ’āˆ«_(āˆ’5)^(āˆ’2)ā–’怖š‘„š‘‘š‘„āˆ’怗 āˆ«_(āˆ’5)^(āˆ’2)ā–’2š‘‘š‘„+āˆ«_(āˆ’2)^5ā–’š‘„š‘‘š‘„+āˆ«_(āˆ’2)^5ā–’2š‘‘š‘„ =āˆ’[š‘„^2/2]_(āˆ’5)^(āˆ’2)āˆ’2[š‘„]_(āˆ’5)^(āˆ’2)+[š‘„^2/2]_(āˆ’2)^5+2[š‘„]_(āˆ’2)^5 =āˆ’(((āˆ’2)^2 āˆ’ (āˆ’5)^2)/2)āˆ’2[āˆ’2āˆ’(āˆ’5)]+[((5)^2 āˆ’ (āˆ’2)^2)/2] +2 [5āˆ’(āˆ’2)] =āˆ’((4 āˆ’ 25)/2)āˆ’2[āˆ’2+5]+[(25 āˆ’ 4)/2]+2[5+2] =āˆ’((āˆ’21)/2)āˆ’2[3]+21/2+2[7] =21/2+21/2āˆ’6+14 =42/2+8 = 21+8 = šŸšŸ—

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