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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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