Unformatted text preview: MATH 32B: MIDTERM 1 REVIEW PROBLEMS Problem 1. Find the average value of 2x + y 2 over the triangle bounded by the lines y = x,
y = 2 − x, and y = 0.
Problem 2. Evaluate 11
0 0 xye dy dx. Problem 3. Find the volume of the solid cut oﬀ by the plane x + y + z = 1 in the ﬁrst
Problem 4. Find the volume of the solid between the cone z =
x2 + y 2 + z 2 = 1. x2 + y 2 and the sphere Problem 5. Find the center of mass of a lamina in the ﬁrst quadrant bounded by the curve
y = 1 − x2 with density function ρ(x, y ) = 2 + x.
Problem 6. Find the volume of the ﬁgure bounded above by the surface z = 2 + x2 + y 2
above the region in the plane inside of the circle with radius 2 and center at (0, 2).
Problem 7. Evaluate 1 2x 2
0 2xyz dz dy dx.
0x Problem 8. Write the equation x2 + y 2 = 2y in cylindrical coordinates.
Problem 9. Evaluate
centered at the origin. H (9 − x2 − y 2 ) dV , where H is the upper hemisphere of radius 3 Problem 10. Show that lima→∞
x2 + y 2 + z 2 e−(x
sphere centered at the origin with radius a. 1 2 +y 2 +z 2 ) dV = 2π , where Sa is the ...
View Full Document
This note was uploaded on 06/03/2011 for the course PHYSICS 1B 1b taught by Professor Corbin during the Winter '10 term at UCLA.
- Winter '10