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Area bounded by curve and horizontal or vertical line
Ex 8.1, 7
Ex 8.1, 1 You are here
Ex 8.1, 11
Example 11
Ex 8.1, 2 Important
Ex 8.1, 8 Important
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. 29, 2021 by Teachoo
Ex 8.1, 1 Find the area of the region bounded by the curve π¦2 = π₯ and the lines π₯ = 1, π₯ = 4 and the π₯-axis in ο»Ώthe first quadrant.Let AB represent line π₯=1 CD represent line π₯=4 & CBOAD represent the curve π¦^2=π₯ Since we need area in the first quadrant We have to find area of BCFE Area of BCFE = β«_π^πβπ . π π So, we need to calculate β«_π^πβπ . π π We know that π¦^2=π₯ Taking square root on both sides β΄ π¦=Β±βπ₯ Since BCEF is in 1st Quadrant β΄ π=βπ Area of BCFE = β«_1^4βπ¦ . ππ₯ = β«_π^πββπ . π π = β«_1^4βγ(π₯)^(1/2) ππ₯γ = [π₯^(1/2+1)/(1/2 +1)]_1^4 = [ π₯^(3/2)/(3/2) ]_1^4 = π/π [π^(π/π) ]_π^π = 2/3 {(4)^(3/2)β(1)^(3/2) } = 2/3 {[(4)^(1/2) ]^3β1} = π/π {(π)^πβπ} = 2/3 [8β1] = 2/3 Γ 7 = 14/3 β΄ Thus Required Area = ππ/π square units