The volume of the solid obtained by rotating the region bounded by the curves `y^2=x` and `y=x^2` about y = 1, can be evaluated using the washer method, such that:

`V = int_a^b pi*(f^2(x) - g^2(x))dx`

You need to find the endpoint of interval, hence, you need to solve for...

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The volume of the solid obtained by rotating the region bounded by the curves `y^2=x` and `y=x^2` about y = 1, can be evaluated using the washer method, such that:

`V = int_a^b pi*(f^2(x) - g^2(x))dx`

You need to find the endpoint of interval, hence, you need to solve for x the following equation, such that:

`sqrt x = x^2 => x - x^4 = 0 => x(1 - x^3) = 0 => x = 0` and `x = 1`

You need to notice that `x^2 < sqrt x` on [0,1], such that:

`V = int_0^1 pi*(((sqrt x) - 1)^2 - (x^2 - 1)^2)dx`

`V = pi*int_0^1 (x- 2sqrt x + 1)dx - pi*int_0^1 (x^4-2x^2 + 1)dx`

`V = (pi*x^2/2 - (4/3)pi*x^(3/2) + pi*x - pi*x^5/5 + 2pi*x^3/3 - pi*x)|_0^1`

`V = pi*1^2/2 - (4/3)pi*1^(3/2) - pi*1^5/5 + 2pi*1^3/3 - 0`

`V = pi/2 + (4pi)/3 - pi/5 - (2pi)/3`

`V = pi/2 + (2pi)/3 - pi/5`

`V = (15pi + 20pi - 6pi)/30`

`V = (29pi)/30`

**Hence, evaluating the volume of the solid obtained by rotating the region bounded by the curves `y^2=x , y=x^2` about y = 1 , using the washer method, yields `V = (29pi)/30.` ` ` **