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

In summary, the conversation is about finding the area bounded by the equations y^2=x and y=x=2. The first rule is to carefully check the problem as the question may not say "y=x=2" and it could be different equations. The second rule is to draw a picture to visualize the problem. It is mentioned that y^2=x is a parabola with the x-axis as its axis and y=x-2 is a line that intersects the parabola at x=y^2=y+2. The final step is to solve the equation to find the area.
  • #1
hytuoc
26
0
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
 
Last edited:
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  • #2
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.
 
  • #3
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.)
 

1. What is the equation for this area?

The equation for this area is y^2=x and y=x=2.

2. How do I find the area bounded by y^2=x and y=x=2?

To find the area bounded by y^2=x and y=x=2, you can use the formula for the area of a region between two curves. First, set the two equations equal to each other to find the points of intersection. Then, integrate the difference of the two functions over the interval between those points.

3. Can you explain the concept of "bounded by" in this context?

In mathematics, "bounded by" refers to the region enclosed by two curves or lines. In this case, the area bounded by y^2=x and y=x=2 is the region between these two curves.

4. What is the significance of finding this area?

Finding the area bounded by y^2=x and y=x=2 can have practical applications in real-world scenarios, such as calculating the area of a shape or determining the volume of a solid. It also helps with understanding and visualizing mathematical concepts.

5. Are there any alternative methods for finding this area?

Yes, there are alternative methods for finding the area bounded by y^2=x and y=x=2. For example, you can use the geometric approach of dividing the region into smaller shapes and calculating their individual areas. You can also use software or graphing calculators to visualize and approximate the area.

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