Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Area bounded by curve and horizontal or vertical line
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Area bounded by curve and horizontal or vertical line
Last updated at May 29, 2023 by Teachoo
Question 2 Find the area of the region bounded by y2 = 9π₯, π₯ = 2, π₯ = 4 and the π₯-axis in the first quadrant. Given curve π¦^2=9π₯ We have to find area between x = 2 and x = 4 β΄ We have to find area of BCFE Area of BCFE = β«_2^4βγπ¦ .γ ππ₯ We know that π¦^2=9π₯ Taking square root on both sides π¦=Β±β9π₯ π¦=Β±3βπ₯ Since BCFE is in 1st Quadrant We take positive value of y β΄ π¦=3βπ₯ Area of BCFE = β«_2^4βγπ¦ .γ ππ₯ = 3β«_2^4ββπ₯ ππ₯ = 3β«_2^4βγ(π₯)^(1/2) ππ₯γ = 3 [π₯^(1/2 + 1)/(1/2 + 1 )]_2^4 = 3 [π₯^(3/2 )/(3/2)]_2^4 = 3 Γ 2/3 [π₯^(3/2) ]_2^4 = 2 [(4)^(3/2 )β(2)^(3/2) ] = 2 [((4)^(1/2) )^3β((2)^(1/2) )^3 ] = 2 [(2)^3β(β2)^3 ] = 2 [8 β2β2] = 16 β 4β2 Thus, Area = 16 β 4βπ square units