Ex 7.4, 25 - Integration dx / root 9x - 4x^2 equals (A) 1/9 sin-1

Ex 7.4, 25 - Chapter 7 Class 12 Integrals - Part 2
Ex 7.4, 25 - Chapter 7 Class 12 Integrals - Part 3

Go Ad-free

Transcript

Ex 7.4, 25 ∫1▒𝑑π‘₯/√(9π‘₯ βˆ’ 4π‘₯^2 ) equals A. 1/9 sinβˆ’1 ((9π‘₯ βˆ’ 8)/8) + C B. 1/9 sinβˆ’1 ((8π‘₯ βˆ’ 9)/9) + C C. 1/3 sinβˆ’1 ((9π‘₯ βˆ’ 8)/8) + C D. 1/2 sinβˆ’1 ((9π‘₯ βˆ’ 8)/8) + C ∫1▒𝑑π‘₯/√(9π‘₯ βˆ’ 4π‘₯^2 ) =∫1▒𝑑π‘₯/√(βˆ’4(π‘₯^2 βˆ’ 9/4 π‘₯) ) =∫1▒𝑑π‘₯/√(βˆ’4(π‘₯^2 βˆ’ 2(π‘₯) (9/8)) ) (Taking βˆ’4 common) =∫1▒𝑑π‘₯/√(βˆ’4[π‘₯^2 βˆ’ 2(π‘₯) (9/8) + (9/8)^2βˆ’ (9/8)^2 ] ) =∫1▒𝑑π‘₯/√(βˆ’4[(π‘₯ βˆ’ 9/8)^2βˆ’ (9/8)^2 ] ) =∫1▒𝑑π‘₯/√(4[(9/8)^2 βˆ’ (π‘₯ βˆ’ 9/8)^2 ] ) =∫1▒𝑑π‘₯/(√4 √((9/8)^2 βˆ’ (π‘₯ βˆ’ 9/8)^2 )) =1/2 ∫1▒𝑑π‘₯/√((9/8)^2 βˆ’ (π‘₯ βˆ’ 9/8)^2 ) It is of form ∫1▒𝑑π‘₯/√(π‘Ž^2 βˆ’ π‘₯^2 ) =sin^(βˆ’1)⁑〖π‘₯/π‘Žγ€— +𝐢1 ∴ Replacing π‘₯ by (π‘₯βˆ’ 9/8) and π‘Ž by 9/8 , we get =1/2 [sin^(βˆ’1)⁑〖(π‘₯ βˆ’ 9/8)/(9/8)γ€— +𝐢1] =1/2 sin^(βˆ’1)⁑[(π‘₯ βˆ’ 9/8)/(9/8)] +𝐢 =1/2 sin^(βˆ’1)⁑〖((8π‘₯ βˆ’ 9)/8)/(9/8)γ€— +𝐢 =1/2 sin^(βˆ’1)⁑〖(8π‘₯ βˆ’ 9)/9γ€— +𝐢 ∴ Option B is correct answer

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo