CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 2024 by Teachoo
This question is similar to Chapter 8 Class 12 Application of Integrals - Examples
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Question 18 A student observes an open-air Honeybee nest on the branch of a tree, whose plane figure is parabolic shape given by 𝑥^2=4𝑦. Then the area (in sq units) of the region bounded by parabola 𝑥^2=4𝑦 and the line 𝑦=4 is (A) 32/3 (B) 64/3 (C) 128/3 (D) 256/3Given that y = 4 Let Line AB represent y = 4 Also, Let AOB represent x2 = 4y We have to find area of AOBA Area of AOBA = 2 × Area BONB = 2∫1_𝟎^𝟒▒〖𝒙 𝒅𝒚〗 We know that 𝑥^2= 4𝑦 𝑥 = ± √4𝑦 𝑥 = ± 2√𝑦 Since BONB is in first quadrant we use x = +𝟐√𝒚 Area of AOBA = 2∫1_0^4▒〖𝑥 𝑑𝑦〗 = 2∫1_0^4▒〖2√𝑦 𝑑𝑦〗 = 2 × 2∫1_0^4▒〖〖(𝑦)^(1/2)〗^ 𝑜𝑦〗 = 4 [𝑦^(1/2 + 1)/(1/2 + 1)]_0^4 = 4[𝑦^((1 + 2)/2 )/((1 + 2)/2)]_0^4 = 4[𝑦^(3/2 )/(3/2)]_0^4 = 4 × 2/3 [𝑦^(3/2 ) ]_0^4 = 8/3 〖[(4)〗^(3/2 )−0] = 8/3 [〖(2^2)〗^(3/2 ) ] = 8/3 × 23 = 8/3 × 8 = 𝟔𝟒/𝟑 So, the correct answer is (B)
