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Find the area of the region bounded by ...

Find the area of the region bounded by the curve `y^2= x`and the lines `x = 1, x = 4`and the x-axis.

Text Solution

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`y^(2)=x` is a symmetric curve about X-axis. ABCDA is the region bounded by `x=1, x=4` and `y^(2)=x` and X-axis.

Required area `=` area of ABCDA
`=int_(1)^(4)|y|dx=int_(1)^(4)sqrt(x)dx`
`=[(x^(3//2))/(3//2)]_(1)^(4)=(2)/(3)[4^(3//2)-1^(3//2)]`
`=(2)/(3)(8-1)=(14)/(3)` sq. units.
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