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Hard Calculus Problem?
Find the area if the region enclosed by the curve SQUAREROOT (x) + SQUAREROOT (y) = 1 and x=0 and y=0
1 Answer
- HemantLv 71 decade agoFavorite Answer
Curve : √x + √y = 1 ..... (1)
y = 0 ... => ... √x + 0 = 1 ... => ... x = 1
The req'd region is bounded by the ordinates
at x = 0 and x = 1, and the X-axis. .................... (2)
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Also, from (1),
√y = 1 - √x
(√y)² = ( 1 - √x )²
y = 1 - 2·√x + x ............... (3)
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From (2) and (3), the req'd area is
= ∫ y dx .... on [0,1]
= ∫ ( 1 - 2√x + x ) dx .... on [0,1]
= [ x - ( 4·x·√x / 3 ) + ( x² / 2 ) ] .... on [0,1]
= [ 1 - ( 4/3 ) + ( 1/2 ) ] - [ 0 ]
= ( 6 - 8 + 3 ) / 6
= ( 1/6 ) sq. units ........................... Ans.
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Happy To Help !
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