Triple integral in cylindrical coordinates?

You can do this by spherical or cylindrical coordinates.

Looks like the limits are given in cylindrical but its easer to do due to this:

x^2+y^2+z^2 = p^2 for spherical

when converting remember to put in the jacobian p^2sinω

given that

int int int p^2 p^2sinω dp dθ dω

recalculate the limits based on r = 0 to 4 θ=π/4 to 3π/4 z= -1 to 1

use spherical coordinates to set the new limits and integrate.

if you dont like this method, you can use cylindrical coordinates

r dzdrdθ as the jacobian.

int int int ((rcosθ)^2+(rsinθ)^2+z^2) r dz dr dθ

the order would be int π/4 to 3π/4, int 0 to 4, int -1 to 1

two ways there you go.

Not going to integrate it for you. You should be comfortable with integration if you're at multivariable calc. Setup of the problem is whats focused on this course.

the cost of the essential is 0. Even with out computing something, word that the forged is symmetric. in case you placed a reflect alongside the xz-airplane, you will see the comparable sturdy to the left and precise. through fact the integrand is y, the area for y > 0 thoroughly cancels the area for y < 0. At any fee, the obstacles of integration in cylindrical coordinates are 0 ? z ? rcos?+ 6, 2 ? r ? ?(6), 0 ? ? ? 2?. The differential quantity element is r dz dr d? and the integrand is r sin?. 2? ?6 rcos? + 6 ? ? ? r² sin? dz dr d? = 0. 0 2 0