Example 24 - Chapter 7 Class 12 Integrals

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Example 24 - Find integral root 3 - 2x - x^2 dx - Teachoo

Example 24 - Chapter 7 Class 12 Integrals - Part 2

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Example 24 Find āˆ«1ā–’āˆš(3āˆ’2š‘„āˆ’š‘„^2 ) š‘‘š‘„ āˆ«1ā–’怖āˆš(3āˆ’2š‘„āˆ’š‘„^2 ) š‘‘š‘„怗 =āˆ«1ā–’āˆš(3āˆ’(2š‘„+š‘„^2 ) ) š‘‘š‘„ Adding and Subtracting 1^2 =āˆ«1ā–’āˆš(3āˆ’(š‘„^2+2š‘„+1^2āˆ’1^2 ) ) š‘‘š‘„ =āˆ«1ā–’āˆš(3āˆ’(š‘„^2+2š‘„+1^2 )+1) š‘‘š‘„ =āˆ«1ā–’āˆš(3+1āˆ’(š‘„^2+2š‘„+1^2 ) ) š‘‘š‘„ =āˆ«1ā–’āˆš(4āˆ’(š‘„^2+2š‘„+1^2 ) ) š‘‘š‘„ =āˆ«1ā–’āˆš(2^2āˆ’(š‘„+1)^2 ) š‘‘š‘„ It is of the form āˆ«1ā–’怖āˆš(š‘Ž^2āˆ’š‘„^2 ) š‘‘š‘„=1/2 š‘„āˆš(š‘Ž^2āˆ’š‘„^2 )+š‘Ž^2/2 š‘ š‘–š‘›^(āˆ’1) š‘„/š‘Ž+š¶ć€— Replacing a with 2 and š‘„ with (š‘„+1) =1/2 (š‘„+1) āˆš(2^2āˆ’(š‘„+1)^2 )+2^2/2 š‘ š‘–š‘›^(āˆ’1) ((š‘„ + 1))/2+š¶ =1/2 (š‘„+1) āˆš(4āˆ’(š‘„^2+1^2+2š‘„))+2š‘ š‘–š‘›^(āˆ’1) ((š‘„ + 1))/2+š¶ =šŸ/šŸ (š’™+šŸ) āˆš(šŸ‘āˆ’šŸš’™āˆ’š’™^šŸ )+šŸ š’”š’Šš’^(āˆ’šŸ) ((š’™ + šŸ))/šŸ+š‘Ŗ

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