Chapter 7 Class 12 Integrals

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Ex 7.7, 11 - Chapter 7 Class 12 Integrals (Important Question)

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Ex 7.7, 11 - Integrate root x2 - 8x + 7 dx - Class 12 - Ex 7.7

Ex 7.7, 11 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.7, 11 āˆ«1ā–’怖āˆš(š‘„2 āˆ’8š‘„+7) " " 怗 š‘‘š‘„ 1/2 (x - 4)āˆš(š‘„2 āˆ’8š‘„+7) + 9 log |š‘„āˆ’4+āˆš(š‘„2āˆ’8š‘„+7)| + C 1/2 (x + 4)āˆš(š‘„2 āˆ’8š‘„+7) + 9 log |š‘„+4+āˆš(š‘„2āˆ’8š‘„+7)| + C 1/2 (x - 4)āˆš(š‘„2 āˆ’8š‘„+7) - 3āˆš2 log |š‘„āˆ’4+āˆš(š‘„2āˆ’8š‘„+7)| + C 1/2 (x - 4)āˆš(š‘„2 āˆ’8š‘„+7) + 9/2 log |š‘„āˆ’4+āˆš(š‘„2āˆ’8š‘„+7)| + C āˆ«1ā–’怖āˆš(š‘„^2āˆ’8š‘„+7) š‘‘š‘„怗 =āˆ«1ā–’怖āˆš(š‘„^2āˆ’2(4)(š‘„)+7) š‘‘š‘„怗 =āˆ«1ā–’怖āˆš(š‘„^2āˆ’2(4)(š‘„) 怖+(4)怗^2āˆ’(4)^2+7) š‘‘š‘„怗 =āˆ«1ā–’怖āˆš((š‘„āˆ’4)^2āˆ’16+7) š‘‘š‘„怗 =āˆ«1ā–’怖āˆš((š‘„āˆ’4)^2āˆ’9 ) š‘‘š‘„怗 =āˆ«1ā–’怖āˆš((š‘„āˆ’4)^2āˆ’(3)^2 ) š‘‘š‘„怗 =(š‘„ āˆ’ 4)/2 āˆš((š‘„āˆ’4)^2āˆ’(3)^2 )āˆ’(3)^2/2 š‘™š‘œš‘”|š‘„āˆ’4+āˆš((š‘„āˆ’4)^2āˆ’(3)^2 )|+š¶ =(š‘„ āˆ’ 4)/2 āˆš(š‘„^2āˆ’8š‘„+16āˆ’9 )āˆ’9/2 š‘™š‘œš‘”|š‘„āˆ’4+āˆš(š‘„^2āˆ’8š‘„+16āˆ’9)|+š¶ =(š‘„ āˆ’ 4)/2 āˆš(š‘„^2āˆ’8š‘„+7)āˆ’9/2 š‘™š‘œš‘”|š‘„āˆ’4+āˆš(š‘„^2āˆ’8š‘„+7)|+š¶ āˆ“ Option (D) is correct. It is of the form āˆ«1ā–’怖āˆš(š‘„^2āˆ’š‘Ž^2 ) š‘‘š‘„=š‘„/2 āˆš(š‘„^2āˆ’š‘Ž^2 )āˆ’š‘Ž^2/2 š‘™š‘œš‘”|š‘„+āˆš(š‘„^2āˆ’š‘Ž^2 )|+š¶ć€— āˆ“ Replacing š‘„ by š‘„āˆ’4 and a by 3 , we get

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