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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

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  • Hemant
    Lv 7
    1 decade ago
    Favorite 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)

    ..................................................................................................................................................

    Also, from (1),

    √y = 1 - √x

    (√y)² = ( 1 - √x )²

    y = 1 - 2·√x + x ............... (3)

    .................................................................................................................................................

    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.

    .................................................................................................................................................

    Happy To Help !

    ..................................................................................................................................................

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