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Area bounded by curve and horizontal or vertical line
Ex 8.1, 7
Ex 8.1, 1
Ex 8.1, 11
Example 11
Ex 8.1, 2 Important
Ex 8.1, 8 Important You are here
Example 3
Misc 3
Ex 8.1, 13 (MCQ) Important
Misc 1 (i)
Ex 8.1, 3
Example 5 Important
Misc 5 Important
Example 13 Important Deleted for CBSE Board 2023 Exams
Example 12
Misc 16 (MCQ)
Misc 17 (MCQ) Important
Area bounded by curve and horizontal or vertical line
Last updated at Dec. 12, 2019 by Teachoo
Ex 8.1, 8 The area between π₯=π¦2 and π₯ = 4 is divided into two equal parts by the line π₯=π, find the value of a. Given curve π¦^2=π₯ Let AB represent the line π₯=π CD represent the line π₯=4 Since the line π₯=π divides the region into two equal parts β΄ Area of OBA = Area of ABCD 2 Γ β«_0^πβγπ¦ ππ₯γ="2 Γ" β«_π^4βγπ¦ ππ₯γ β«_π^πβγπ π πγ=β«_π^πβγπ π πγ Now, y2 = x y = Β± βπ₯ Since, the curve is symmetric about x-axis we can take either positive or negative value of π¦ So, lets take π¦=βπ₯ Now, From (1) β«_0^πβγπ¦ ππ₯γ=β«_π^4βγπ¦ ππ₯γ β«_0^πββπ₯ ππ₯=β«_π^4ββπ₯ ππ₯ [π₯^(1/2 + 1)/(1/2 + 1)]_0^π=[π₯^(1/2+1)/(1/2+1)]_π^4 [π₯^((1+2)/2) ]_0^π=[π₯^((1+2)/2) ]_π^4 [π₯^(3/2) ]_0^π=[π₯^(3/2) ]_π^4 (π)^(3/2)β0=(4)^(3/2)β(π)^(3/2) 2(π)^(3/2)=(4)^(3/2) Taking γ2/3γ^π‘β root on both sides (2)^(2/3) π^(3/2 Γ 2/3)=4^(3/2 Γ 2/3) (2)^(2/3) π=4 π=(2)^2/(2)^(2/3) π=(2)^(2 β 2/3) π=(2)^((6 β 2)/3) π=(2)^(4/3) π=(2)^(2 Γ 2/3) π=[2^2 ]^(2/3) π=(π)^(π/π) So, value of a is (4)^(2/3)