Exam 4 Spring11

# Exam 4 Spring11 - Z 3 Z √ 9-y f x,y dxdy 9 SET UP(Do not...

This preview shows pages 1–4. Sign up to view the full content.

MAC 2313-EXAM 4 NAME UF ID 1. A lamina occupies the part of the disk x 2 + y 2 1 in the ﬁrst quadrant. Find the mass if the density at any point is proportional to its distance to the y axis. 2. SET UP (Do not evaluate) the integral Z 2 - 2 Z 4 - y 2 - 4 - y 2 Z 2 x 2 + y 2 ( x 2 + y 2 ) z dz dxdy in cylindrical coordinates. 3. Let H be the region between the sphere x 2 + y 2 + z 2 = 4 and x 2 + y 2 + z 2 = 9 in the ﬁrst octant then the region H in sphererical coordinates is given by . H = { ( ρ,θ.φ ) : } 4. Let E be the region bounded by the paraboloid z = 4 x 2 + 4 y 2 and the plane z = 4, then the region E in Cartesian coordinates is given by E = { ( x,y,z ) : } 5. According to Fubini’s theorem, if f is continuous on the rectangle R = { ( x,y ) | a x b,c y d } then ZZ R f ( x,y ) dA = = 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6. Calculate the iterated integral Z 2 0 Z π 0 r sin 2 θdθdr . 7. Given the integral ZZ D ( x + y ) dA = Z 1 0 Z 2 - y 2 y ( x + y ) dxdy , the region D in polar coordinates is given by D = { ( r,θ ) : } 8. Change the order of integration for

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Z 3 Z √ 9-y f ( x,y ) dxdy . 9. SET UP (Do not evaluate) the integral Z Z D ( x + y ) dA , where D is bounded by y = √ x and y = x 2 . 10. If R = 0 ≤ x ≤ 6 , ≤ y ≤ 4 } and m = 3 ,n = 2 and we would like to use the upper right corners of the squares, write all sample points that would be used to calculate the double Riemmann sum. 2 MAC 2313 — EXAM 4 Free Response NAME UF ID YOU MUST SHOW ALL OF YOUR WORK TO RECEIVE CREDIT!! 1. Evaluate the integral Z 1 Z √ 2-y 2 y ( x + y ) dxdy 3 2. Find the volume of the solid that lies within the sphere x 2 + y 2 + z 2 = 4, above the xy plane, and below the cone z = p x 2 + y 2 . 4...
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Exam 4 Spring11 - Z 3 Z √ 9-y f x,y dxdy 9 SET UP(Do not...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online