√1-x² L [²₁²² [² (2²³ + 1²³) dz dy de to cylindrical coordinates and evaluate the result. (Think about why converting to cylindrical coordinates makes sense.) 2. Convert the integral

Use spherical coordinates.Evaluate∭e ^ (x ^ 2 + y ^ 2 + z ^ 2) dV,where E is inside the sphere x ^ 2 + y ^ 2 + z ^ 2 = 25 in the first octant.

Locate the centroid of the solid generated when the area of x^2 + y^2 = a^2 in the first quadrant and the fourth quadrant by 2x - y = 2a and x = 0 about x = 0, a. (0, 2a/3) b. (0,-2a/3) c. (0,-a/16) d, (0, a/16)

What is the intersection of z = x^2+ y^2 with the cylinder (x-1)^2+y^2=1?

Find normal line (parametric form) to the surface x^2 − 4y^2 + z^2 + y = 27 at the point (5, 1, −3).

A solid lies inside the sphere x^2 + y^2 + z^2 = 6z and outside the cone z=sqrt(x^2+y^2). Write a description of the solid in terms of inequalities involving spherical coordinates

(4) Express the surface of the conez=2*sqrt(x^2+y^2)using equations (or inequalities) in...(a) cylindrical coordinates.(b) spherical coordinates.

Laplace of t^2 using integration by parts twice