CBSE Class 12 Sample Paper for 2021 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

## Find the area of the region bounded by the parabola π¦ 2 = 8π₯ and the line π₯ = 2.

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Note : This is similar to Ex 8.1, 11 of NCERT β Chapter 8 Class 12 Applications of Integration

Check the answer here https:// www.teachoo.com /3335/730/Ex-8.1--11---Find-area-bounded-by-y2--4x-and-line-x--3/category/Ex-8.1/

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### Transcript

Question 24 Find the area of the region bounded by the parabola π¦2 = 8π₯ and the line π₯ = 2. Let AB represents the line π₯=2 and AOB represent the curve π¦^2=8π₯ Area of AOBC = 2 Γ [Area of AOC] = 2 Γ β«_π^πβγπ.ππγ We know that π¦^2=8π₯ π¦=Β±β8π₯ π=Β±πβππ As AOC is in 1st Quadrant β΄ π¦=2β2 βπ₯ β΄ Area of AOBC = 2 Γ β«_0^2βγπ¦.ππ₯γ = 2 β«_0^2βγ2β2 βπ₯ ππ₯γ = 4β2 β«_0^2βγβπ₯ ππ₯γ = 4β2 β«_0^2βγ(π₯)^(1/2) ππ₯γ = 4β2 [π₯^(1/2+1)/(1/2+1)]_0^2 =4β2 Γ 2/3 [π₯^(3/2) ]_0^2 = (8β2)/3 [(2)^(3/2)β0] = (8β2)/3 [(2)^(3/2)β0] =(8β2)/3 [(β2)^3 ] =(8β2)/3 [ β2 Γ β2 Γ β2 ] = 8/3 [ 2 Γ 2] = ππ/π square units β΄ Required Area = ππ/π square units