Spherical and Cylindrical Coordinates – Between a sphere and a cone – Exercise 4619 Post category:Spherical and Cylindrical Coordinates Post comments:0 Comments Exercise Calculate the integral ∫01dx∫01−x2dy∫x2+y22−x2−y2z2dz\int_0^1 dx\int_0^{\sqrt{1-x^2}} dy\int_{\sqrt{x^2+y^2}}^{2-x^2-y^2} z^2 dz∫01dx∫01−x2dy∫x2+y22−x2−y2z2dz Final Answer Show final answer ∫01dx∫01−x2dy∫x2+y22−x2−y2z2dz=π(22−1)15\int_0^1 dx\int_0^{\sqrt{1-x^2}} dy\int_{\sqrt{x^2+y^2}}^{2-x^2-y^2} z^2 dz=\frac{\pi(2\sqrt{2}-1)}{15}∫01dx∫01−x2dy∫x2+y22−x2−y2z2dz=15π(22−1) Solution Coming soon… Share with Friends Read more articles Next PostSpherical and Cylindrical Coordinates – On an ellipse – Exercise 4620 You Might Also Like Spherical and Cylindrical Coordinates – On a sphere – Exercise 4606 April 15, 2019 Spherical and Cylindrical Coordinates – On a cone – Exercise 4611 April 15, 2019 Spherical and Cylindrical Coordinates – On a sphere – Exercise 4613 April 15, 2019 Spherical and Cylindrical Coordinates – On a cone – Exercise 4617 April 15, 2019 Spherical and Cylindrical Coordinates – On an ellipse – Exercise 4620 April 15, 2019 Leave a Reply Cancel replyCommentEnter your name or username to comment Enter your email address to comment Enter your website URL (optional) Δ