Question 4 - NCERT Exemplar MCQ - Chapter 7 Class 12 Integrals

Last updated at December 14, 2024 by

āˆ« (a + c)^(b + c)Ā  f(x) dx is equal to

(A) āˆ« (a )^(b)Ā  f(x - c)Ā  Ā 

(B) āˆ« (a )^(b) f(x + c) dxĀ 

(C) āˆ«(a )^(b) f(x) dxĀ  Ā Ā 

(D) āˆ« (a - c)^(b - c) (x) dxĀ  Ā Ā 

This question is similar to Misc 43 (MCQ) - Chapter 7 Class 12 - Integrals

Ā 

[Integrals - MCQ] Intgeral āˆ« š‘ + š‘ š‘Ž + š‘ š‘“(š‘„) š‘‘š‘„ is equal to - NCERT Exemplar MCQ

part 2 - Question 4 - NCERT Exemplar MCQ - Serial order wise - Chapter 7 Class 12 Integrals

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Question 4 āˆ«1_(š‘Ž + š‘)^(š‘ + š‘)ā–’怖 š‘“(š‘„) š‘‘š‘„怗 is equal to āˆ«1_(š‘Ž )^(š‘ )ā–’怖š‘“(š‘„āˆ’š‘) š‘‘š‘„怗 (B) āˆ«1_(š‘Ž )^(š‘ )ā–’怖š‘“(š‘„+š‘) š‘‘š‘„怗 (C) āˆ«1_(š‘Ž )^(š‘ )ā–’怖š‘“(š‘„) š‘‘š‘„怗 (D) āˆ«1_(š‘Ž āˆ’š‘)^(š‘āˆ’š‘ )ā–’怖š‘“(š‘„) š‘‘š‘„怗 āˆ«1_(š‘Ž + š‘)^(š‘ + š‘)ā–’怖 š‘“(š‘„) š‘‘š‘„怗 Putting š’™=š’•+š’„ Differentiating w.r.t. š‘„ š‘‘š‘„=š‘‘š‘” Now, when š’™ varies from a + c to b + c then š’• varies from a to b Therefore āˆ«1_(š‘Ž + š‘)^(š‘ + š‘)ā–’怖 š‘“(š‘„) š‘‘š‘„怗 =āˆ«_š‘Ž^š‘ā–’š‘“(š‘”+š‘)š‘‘š‘” Changing variables ā€“ using Property 1 =āˆ«_š’‚^š’ƒā–’š’‡(š’™+š’„)š’…š’™ So, the correct answer is (b)

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