Example 9 (iii) - Chapter 7 Class 12 Integrals

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Example 9 - Chapter 7 Class 12 Integrals - Part 7

Example 9 - Chapter 7 Class 12 Integrals - Part 8

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Example 9 Find the following integrals: (iii) āˆ«1ā–’š‘‘š‘„/(āˆš(5š‘„^2 āˆ’ 2š‘„) ) āˆ«1ā–’š‘‘š‘„/(āˆš(5š‘„^2 āˆ’ 2š‘„) ) = āˆ«1ā–’š‘‘š‘„/(āˆš(5(š‘„^2 āˆ’ 2/5 š‘„) ) ) = āˆ«1ā–’š‘‘š‘„/(āˆš(5(š‘„^2 āˆ’ 2(š‘„)(1/5)) ) ) = āˆ«1ā–’š‘‘š‘„/(āˆš(5(š‘„^2 āˆ’ 2(š‘„)(1/5) + (1/5)^2āˆ’ (1/5)^2 ) ) ) = āˆ«1ā–’š‘‘š‘„/(āˆš(5[(š‘„ āˆ’ 1/5)^2āˆ’(1/5)^2 ] ) ) = āˆ«1ā–’š‘‘š‘„/(āˆš5 āˆš((š‘„ āˆ’ 1/5)^2āˆ’(1/5)^2 )) (Taking 5 common) [Adding and subtracting (1/5)^2] = āˆ«1ā–’š‘‘š‘„/(āˆš(5[(š‘„ āˆ’ 1/5)^2āˆ’(1/5)^2 ] ) ) = āˆ«1ā–’š‘‘š‘„/(āˆš5 āˆš((š‘„ āˆ’ 1/5)^2āˆ’(1/5)^2 )) =1/āˆš5 š‘™š‘œš‘”|š‘„āˆ’1/5+āˆš((š‘„āˆ’1/5)^2āˆ’(1/5)^2 )|+š¶ =1/āˆš5 š‘™š‘œš‘”|š‘„āˆ’1/5+āˆš(š‘„^2+(1/5)^2āˆ’2(š‘„)(1/5)āˆ’(1/5)^2 )|+š¶ =šŸ/āˆššŸ“ š’š’š’ˆ|š’™āˆ’šŸ/šŸ“+āˆš(š’™^šŸāˆ’šŸš’™/šŸ“)|+š‘Ŗ It is of form āˆ«1ā–’怖š‘‘š‘„/(āˆš(š‘„^2 āˆ’ š‘Ž^2 ) )=š‘™š‘œš‘”|š‘„+āˆš(š‘„^2āˆ’š‘Ž^2 )|+š¶1怗 Replacing š‘„ by (š‘„āˆ’1/5)š‘Žš‘›š‘‘ š‘Ž š‘š‘¦ 1/5, (Usingāˆš(š‘Ž.š‘)=āˆšš‘Ž āˆšš‘)

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