Suppose f(x, y,z) = x2 + y2 + z2 and W is the solid cylinder with height 7 and base radius 2 that is centered about the z-axis with its base at z = −2. Enter θ as theta. A) As an iterated integral, ∭WfdV = ∫BA∫DC∫FE dzdrdθ with limits of integration.
B) Evaluate the integral.

A)

A = 0       B = 2π

C = 0       D = 2

E = - 2      F = 5

B)

V = 216 π

Step-by-step explanation:

Using cylindrical coordinates

x= rcosθ , y = rsinθ, z = z

Then, dV =rdzdrdθ

where x² + y² + z² = r² + z²

E= ( 0 ≤ θ ≤ 2π, 0 ≤ r ≤ 2, -2 ≤ z ≤ 5 )

∴

A = 0       B = 2π

C = 0       D = 2

E = - 2      F = 5

V = 12π (4 + 14)

V = 12π(18)

V = 216 π

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

stop using this to cheat on home work

step-by-step explanation:

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