# Ex 8.1, 8

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex 8.1, 8 The area between 𝑥=𝑦2 and 𝑥 = 4 is divided into two equal parts by the line 𝑥=𝑎, find the value of a. Let AB represent the line 𝑥=𝑎 CD represent the line 𝑥=4 and CBOAD represent the curve 𝑥= 𝑦2 Since the line 𝑥=𝑎 divides the region into two equal parts ∴ Area of OBA = Area of ABCD 2 × 0𝑎𝑦 𝑑𝑥=2 × 𝑎4𝑦 𝑑𝑥 0𝑎𝑦 𝑑𝑥= 𝑎4𝑦 𝑑𝑥 Now, y2 = x y = ± 𝑥 Since, the curve is symmetric about 𝑥−𝑎𝑥𝑖𝑠 we can take either value of 𝑦 So, lets take 𝑦= 𝑥 ∴ 0𝑎𝑦 𝑑𝑥= 𝑎4𝑦 𝑑𝑥 0𝑎 𝑥𝑑𝑥= 𝑎4 𝑥𝑑𝑥 𝑥 12 + 1 12 + 10𝑎= 𝑥 12+1 12+1𝑎4 𝑥 1+220𝑎= 𝑥 1+22𝑎4 𝑥 320𝑎= 𝑥 32𝑎4 𝑎 32−0= 4 32− 𝑎 32 2 𝑎 32= 4 32 Taking 23𝑡ℎ root on both sides 2 23 𝑎 32 × 23= 4 32 × 23 2 23 𝑎=4 𝑎= 22 2 23 𝑎= 22− 23 𝑎= 2 6−23 𝑎= 2 43 𝑎= 22 × 23 𝑎= 22 23 𝒂= 𝟒 𝟐𝟑

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