CBSE Class 12 Sample Paper for 2026 Boards
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CBSE Class 12 Sample Paper for 2026 Boards
Last updated at Sept. 2, 2025 by Teachoo
This question is similar to Chapter 8 Class 12 Application of Integrals - Ex 8.1
Please check the question here
Transcript
Question 23 (B) Find out the area of shaded region in the enclosed figure. Letβs redraw the figure The curve is π^π=π We have to find area between y = 0 and y = 4 β΄ We have to find area of BNO Area of BNO = β«_π^πβπ π π We know that π₯^2=π¦ Taking square root on both sides π="Β±" βπ Since, BNO is in 1st Quadrant We take positive value of x β΄ π=βπ Area of BCFE = β«_0^4βπ₯ ππ¦ = β«_π^πββπ π π = β«_0^4βγ(π¦)^(1/2) ππ¦γ = [π¦^(3/2)/(3/2)]_0^4 = 2/3 [π¦^(3/2) ]_2^4 = π/π [(π)^(π/π )β(π)^(π/π) ] = 2/3 [(4)^(3/2 ) ] = π/π [π^(π Γπ/π) ] = 2/3 Γ 2^3 = (2 Γ 8)/3 = ππ/π Thus, Area = ππ/π square units Area of BCFE = β«_0^4βπ₯ ππ¦ = β«_π^πββπ π π = β«_0^4βγ(π¦)^(1/2) ππ¦γ = [π¦^(3/2)/(3/2)]_0^4 = 2/3 [π¦^(3/2) ]_2^4 = π/π [(π)^(π/π )β(π)^(π/π) ] = 2/3 [(4)^(3/2 ) ] = π/π [π^(π Γπ/π) ]
