Chapter 7 Class 12 Integrals

Chapter 8 Class 12 Application of Integrals →
Class 12
Important Questions for exams Class 12

Ex 7.8, 22 (MCQ) - Chapter 7 Class 12 Integrals (Important Question)

Last updated at July 14, 2026 by

Ex 7.8, 22 (MCQ) - Direct Integrate dx / 4 + 9x2 from 0 to 2/3 - Ex 7.8

part 2 - Ex 7.8, 22 (MCQ) - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals
part 3 - Ex 7.8, 22 (MCQ) - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals part 4 - Ex 7.8, 22 (MCQ) - Ex 7.8 - Serial order wise - Chapter 7 Class 12 Integrals

Remove Ads Share on WhatsApp

Transcript

Ex 7.8, 22 Choose the correct answer āˆ«_0^(2/3)ā–’š‘‘š‘„/(4 +9š‘„^2 ) equals (A) šœ‹/6 (B) šœ‹/12 (C) šœ‹/24 (D) šœ‹/4 Step 1 :- Let F(š‘„)=āˆ«1ā–’š‘‘š‘„/(4 + 9š‘„^2 ) Divide and multiply the integrate by 4 =āˆ«1ā–’ā–ˆ(š‘‘š‘„@4)/((4 + 9š‘„^2)/4) =1/4 āˆ«1ā–’š‘‘š‘„/(1 + 9/4 š‘„^2 ) =1/4 āˆ«1ā–’š‘‘š‘„/(1 + (3/2 š‘„)^2 ) Put 3/2 š‘„=š‘” Differentiating w.r.t.š‘„ š‘‘(3/2 š‘„)/š‘‘š‘„=š‘‘š‘”/š‘‘š‘„ 3/2=š‘‘š‘”/š‘‘š‘„ š‘‘š‘„=š‘‘š‘”/(3/2) š‘‘š‘„=2/3 š‘‘š‘” Hence 1/4 āˆ«1ā–’怖š‘‘š‘„/(1+(3/2 š‘„)^2 )=1/4 āˆ«1ā–’怖1/(1+š‘”^2 ) 2/3怗 š‘‘š‘”怗 =1/4 Ɨ 2/3 āˆ«1ā–’š‘‘š‘”/(1+š‘”^2 ) =1/6 tan^(āˆ’1)ā”š‘” Putting š‘”=3/2 š‘„ =1/6 tan^(āˆ’1)ā”怖3/2 š‘„怗 Hence F(š‘„)=1/6 tan^(āˆ’1)ā”怖3/2 š‘„怗 Step 2 :- āˆ«_0^(2/3)ā–’怖š‘‘š‘„/(4+9š‘„^2 )=š¹(2/3)āˆ’š¹(0) 怗 =1/6 tan^(āˆ’1)ā”怖(3/2 Ɨ 2/3)āˆ’1/6 tan^(āˆ’1)ā”(0) 怗 =1/6 tan^(āˆ’1)ā”怖(1)āˆ’1/6 tan^(āˆ’1)ā”(0) 怗 =1/6 Ɨ šœ‹/4āˆ’0 =šœ‹/24 āˆµ Option (C) is correct.

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.