Find the area bounded by y^2=x and y=x=2

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SUMMARY

The area bounded by the curves defined by the equations y² = x and y = x = 2 can be determined by first identifying the correct equations. The discussion clarifies that y = x = 2 is likely a misinterpretation and should be y = x - 2 or y - x = 2. To find the area, one must calculate the area under the parabola y² = x and then subtract the area under the line defined by the corrected equation. The intersection points of these curves are found by solving the equation y² - y - 2 = 0.

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How do I do this problem below? Plz guide me step by step or a least show me the correct bounds so I can learn...thanks
***Find the area bounded by y^2=x and y=x=2
Thanks so much
 
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hytuoc said:
How do I do this problem below? Plz guide me step by step or a least show me the correct bounds so I can learn...thanks
***Find the area bounded by y^2=x and y=x=2
Thanks so much


You could always find the are enclosed by the second equation, then you could find the area between the first eqn and the x axis, then you could subract the second area from the first.
 
First rule: check the problem carefully- doubt that the question actually says "y= x= 2". It might well be y= x-2 or y-x= 2 which are very different.

Second rule: draw a picture. y2= x is a parabola (with x-axis as axis),
y= x- 2, which can be written as x= y+2, is a line which crosses the parabola when
x= y2= y+ 2: solve the equation y2- y- 2= 0.
(or, if you mean y-x= 2, x= y-2 so x= y2= y- 2.)
 

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