See image **Evaluate the Triple Integral:**\[\int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{2} (x^2 + y^2) \, dz \, dy \, dx\]**Solution:**This iterated integral is a triple integral over the solid region \( E \).- The region \( E = \{ (x, y, z) \, | \, -2 \leq x \leq 2, \, -\sqrt{4-x^2} \leq y \leq \sqrt{4-x^2}, \, \sqrt{x^2 + y^2} \leq z \leq 2 \} \) - The projection of \( E \) onto the xy-plane is the disk: \( x^2 + y^2 \leq 4 \). - The lower surface of \( E \) is the cone: \( z = \sqrt{x^2 + y^2} \). - The upper surface is the plane \( z = 2 \).This region has a much simpler description in cylindrical coordinates:- \( E = \{ (r, \theta, z) \, | \, 0 \leq \theta \leq 2\pi, \, 0 \leq r \leq 2, \, r \leq z \leq 2 \} \).**Note to Reader:**Set up but do not solve the integral needed using cylindrical coordinates.**Diagrams:**The diagram illustrates the geometric shape of the region \( E \), featuring:1. **Cone:** With a vertex at the origin and extending upwards, its sides represented by \( z = \sqrt{x^2 + y^2} \).2. **Plane:** The top boundary at \( z = 2 \).3. **Cylindrical Representation:** The circular base is centered around the z-axis with a radius of 2, and the cylinder height is cut by the plane and the cone.

Name: See image **Evaluate the Triple Integral:**\[\int_{-2}^{2} \int_{-\sqr
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: See image **Evaluate the Triple Integral:**\[\int_{-2}^{2} \int_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}} \int_{\sqrt{x^2+y^2}}^{2} (x^2 + y^2) \, dz \, dy \, dx\]**Solution:**This iterated integral is a triple integral over the solid region \( E \).- The regio