Given a Continuous Signal FXy X Y2 Evaluate the Following
Get the answer to your homework problem.
Try Numerade free for 7 days
(10 pts) Q # 8 Given f(x,y,2) = 1 - x2 + y2 + 22 and B = {(x,y,2)lx2+y2 +22 < 9,y 2 0,2 2 0} evaluate the triple integral for the region B
Related Question
(a) Express the triple integral SI f (€,y; 2, dVas an iterated integral in spherical coordinates for the given function f and solid region E. (b) Evaluate the iterated integral: 21. f(c,y, 2) = 32+y+ 2
Discussion
You must be signed in to discuss.
Video Transcript
Hi in this question we are given with the function F of X, Y Z. That is equals to under root X squared plus Y squared plus z squared. And first we need to express the triple integral. That is this for F O X, Y Z. In I treated integral in this hypothetical coordinates as we know in this medical coordinates Rose square is equal to X squared plus Y squared plus eight squared. So substituting fx visor as this and replacing this withdrew square. We can write it in terms of the spherical coordinates and this would be equals two triple integral for Andrew to off road square times. Rose square sci fi defi zero and D theta in this we can write it further as to be equals to triple integral. Here we get wrong only and multiplying this with Rose square will result in blue cube sine phi d rho d phi d Theta Here for the limits of rho phi and theta as we know, the limit of integration for row will be the radius of biggest fear to the radius of smaller sphere. In the biggest fear we have the radius R squared is equal to nine. Or we can write our to be equal to three and in the smaller square R squared is equal to four. So are will be equals to two. So our limits for row would be from 2 to 3 and 45 it is from zero to pi and for theta it is from zero to and this is what our I tweeted integral in the spherical coordinates. Now moving on to the B part where we need to solve this integral we can write this to be equals to integration from 0 to 2 pi integration from zero to pi Integration from 2 to 3 Q. D rho sine phi d phi d. Theta. And this would be equals two. Integration from 0 to 2 pi integration from zero to pi here we can write the integration of this as row four upon four limits from toto three. Sine phi defi D Theta now substituting the limits for row into the obtained result we get this to be equals to integration from 0 to 2 pi integration from zero to pi here substituting the limit we get three days to perform a 30.4 minus tourists to perform a 0.4. Close it and not break it sci fi d phi d theta now solving this we get a constant value and let it keep out and this will be equals to 65 by four. Integration from 0 to 2 pi. Now integration of science. Fire defy will be equals two minus costs five. Were the limits from zero to pi D. Theta. Now substituting the limits for here we get 65 by four times integration from 0 to 2 pi minus cost pi minus minus course zero B T to or solving this further we get this to be equals to 65 by four. Integration from 0 to 2 pi minus quantify is minus minus one minus minus one and D theta solving this further, we get 65 by four times one plus one. That is to integration of d theta theta having limits from 0 to 2 pi. Now substituting the limits, we get this to be equals to 65 by four times two into two pi here to to Will cancel this four and we were left with our final answer for the result of the triple integral, which is equals to 655. I hope this answer to be useful to you. Thank you.
Source: https://www.numerade.com/ask/question/10-pts-q-8-given-fxy2-1-x2-y2-22-and-b-xy2lx2y2-22-9y-2-02-2-0-evaluate-the-triple-integral-for-the-region-b-77609/
Post a Comment for "Given a Continuous Signal FXy X Y2 Evaluate the Following"