calculating the double integral for the area bounded

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Compute the double integral which will give the area of the region between $y$-axis, the sphere $(x-2)^2 + (y-4)^2 = z^2$ and the parabola $2y = x^2$. Compute the integral and find the area.



I am unable to find the limits of the integration as I cannot visualize the intersection. Please help me.




calculus




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  • $(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
    – saulspatz
    Jul 26 at 15:17











  • @KeyFlex How did you decide $z=1?$
    – saulspatz
    Jul 26 at 15:19










  • @user108128 Thanks. I ought to have my morning tea before doing this.
    – saulspatz
    Jul 26 at 15:21










  • @Balaji Could you clarify what you mean by the region between the y-axis?
    – AzJ
    Jul 26 at 15:29














up vote
-1
down vote

favorite












Compute the double integral which will give the area of the region between $y$-axis, the sphere $(x-2)^2 + (y-4)^2 = z^2$ and the parabola $2y = x^2$. Compute the integral and find the area.



I am unable to find the limits of the integration as I cannot visualize the intersection. Please help me.




calculus




share|cite|improve this question





















  • $(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
    – saulspatz
    Jul 26 at 15:17











  • @KeyFlex How did you decide $z=1?$
    – saulspatz
    Jul 26 at 15:19










  • @user108128 Thanks. I ought to have my morning tea before doing this.
    – saulspatz
    Jul 26 at 15:21










  • @Balaji Could you clarify what you mean by the region between the y-axis?
    – AzJ
    Jul 26 at 15:29












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











Compute the double integral which will give the area of the region between $y$-axis, the sphere $(x-2)^2 + (y-4)^2 = z^2$ and the parabola $2y = x^2$. Compute the integral and find the area.



I am unable to find the limits of the integration as I cannot visualize the intersection. Please help me.




calculus




share|cite|improve this question













Compute the double integral which will give the area of the region between $y$-axis, the sphere $(x-2)^2 + (y-4)^2 = z^2$ and the parabola $2y = x^2$. Compute the integral and find the area.



I am unable to find the limits of the integration as I cannot visualize the intersection. Please help me.





calculus





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 26 at 15:19
























asked Jul 26 at 15:11









Balaji

6617




6617











  • $(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
    – saulspatz
    Jul 26 at 15:17











  • @KeyFlex How did you decide $z=1?$
    – saulspatz
    Jul 26 at 15:19










  • @user108128 Thanks. I ought to have my morning tea before doing this.
    – saulspatz
    Jul 26 at 15:21










  • @Balaji Could you clarify what you mean by the region between the y-axis?
    – AzJ
    Jul 26 at 15:29
















  • $(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
    – saulspatz
    Jul 26 at 15:17











  • @KeyFlex How did you decide $z=1?$
    – saulspatz
    Jul 26 at 15:19










  • @user108128 Thanks. I ought to have my morning tea before doing this.
    – saulspatz
    Jul 26 at 15:21










  • @Balaji Could you clarify what you mean by the region between the y-axis?
    – AzJ
    Jul 26 at 15:29















$(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
– saulspatz
Jul 26 at 15:17





$(x-2)^2 + (y-4)^2 = z^2$ is the equation of a paraboloid not a circle. How many dimensions are you in?
– saulspatz
Jul 26 at 15:17













@KeyFlex How did you decide $z=1?$
– saulspatz
Jul 26 at 15:19




@KeyFlex How did you decide $z=1?$
– saulspatz
Jul 26 at 15:19












@user108128 Thanks. I ought to have my morning tea before doing this.
– saulspatz
Jul 26 at 15:21




@user108128 Thanks. I ought to have my morning tea before doing this.
– saulspatz
Jul 26 at 15:21












@Balaji Could you clarify what you mean by the region between the y-axis?
– AzJ
Jul 26 at 15:29




@Balaji Could you clarify what you mean by the region between the y-axis?
– AzJ
Jul 26 at 15:29















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