`x = y^4, y = sqrt(2 - x), y = 0` Sketch the region enclosed by the given curves and find its area.

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gsarora17 eNotes educator| Certified Educator

`x=y^4,y=sqrt(2-x), y=0`

Refer the attached image. `x=y^4` is plotted in red color and `y=sqrt(2-x)` is plotted in blue color.The curves intersect at x=y=1.

`y=sqrt(2-x)rArry^2=2-x=>x=2-y^2`

Area of the region enclosed by the given curves A=`int_0^1((2-y^2)-y^4)dy`

`A=int_0^1(2-y^2-y^4)dy`

`A=[2y-y^3/3-y^5/5]_0^1`

`A=(2*1-1^3/3-1^5/5)`

`A=(2-1/3-1/5)`

`A=(30-5-3)/15`

`A=22/15`

 

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