CBSE Class 12 Sample Paper for 2025 Boards
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CBSE Class 12 Sample Paper for 2025 Boards
Last updated at July 25, 2026 by Teachoo
This question is similar to Chapter 8 Class 12 Application of Integrals - Examples
Please check the question hereĀ
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Ā
Transcript
Question 18 A student observes an open-air Honeybee nest on the branch of a tree, whose plane figure is parabolic shape given by š„^2=4š¦. Then the area (in sq units) of the region bounded by parabola š„^2=4š¦ and the line š¦=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 Ć Area BONB = 2ā«1_š^šāćš š šć We know that š„^2= 4š¦ š„ = Ā± ā4š¦ š„ = Ā± 2āš¦ Since BONB is in first quadrant we use x = +šāš Area of AOBA = 2ā«1_0^4āćš„ šš¦ć = 2ā«1_0^4āć2āš¦ šš¦ć = 2 Ć 2ā«1_0^4āćć(š¦)^(1/2)ć^ šš¦ć = 4 [š¦^(1/2 + 1)/(1/2 + 1)]_0^4 = 4[š¦^((1 + 2)/2 )/((1 + 2)/2)]_0^4 = 4[š¦^(3/2 )/(3/2)]_0^4 = 4 Ć 2/3 [š¦^(3/2 ) ]_0^4 = 8/3 ć[(4)ć^(3/2 )ā0] = 8/3 [ć(2^2)ć^(3/2 ) ] = 8/3 Ć 23 = 8/3 Ć 8 = šš/š So, the correct answer is (B)
