Question

(1 point) Express the integral JIJ: f(,y,z)dV as an iterated integral in six diferent ways, where is the solid bounded by z = 0,2 = 4y and zº = 16 – y. 92(3) 1 Torce has bec" f(2,9, 2)dzdydz a = -4 b= 4 91(x) = 0 h1(x,y) = 0 92(2) = 16-x^2 h2(x, y) = 4y 92(y) h(x,y) 2. Ja Jg.(y) Th.(z,y) a = b= 91(y) = h (z,y) = g2(y) = h2(x, y) = 4y 0 3 S. * J* 5121, , 2)dədyd: a be 91() = ht(g, 2) = 92() = h2(y, 2) = 4 S. LO 99 $12, 9, ədədzdy a= b= 91(y) = hiy, z) = 92(y) = h2(y, 2) = 5. S S Juha " $12, 9, 3dydzda a = b= 91(x) = hi(2, 2) = 92(x) = h2(3, ) = 6 SLS s12, 9, )dyded: Jg.(z) Jh,(1,2) a= b= 91() = h1(1, ) = 92(2) = h2(x,x) =

I don't understand how we solve for all the other variations. Can anyone help me out and walk me through the process? I know its quite a long question, but I'd really appreciate it!

Answer 1

6 Here also we will consider &1-2 plane. we have, osz=64. Now, we have find values of a in terms of 2. we had √16-y sxs ſ16.-7 But earlier weo see y depend on 2 cas, 2 sy s 16. So, values of x lie in - ( 16 7 4 5x5 /16- 2 / 2 ię √64-2 u xs √64-2 Hence, region 2 2 É is, {os 2564 – Vor 2 ans Jorz, 254s 16}

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