Math 53 Quiz 7 Name: Problem 1 [5 pts]. Evaluate the integral RRR E x dV where E is the solid enclosed by the curves z =1 - x 2 , z = 0, y = 0, and y = 1 drawn below. Problem 2 [5 pts]. Using integration, find the volume of the hemisphere (half-sphere) enclosed inside the unit sphere x 2 + y 2 + z 2 = 1 and above the z = 0 plane. 1
Problem 1 [5 pts]. Evaluate the integralE x dV where E is the
solid enclosed by the curves z = 1x2, z = 0,
y = 0, and y = 1 drawn below.
Problem 2 [5 pts]. Using integration, find the volume of the
hemisphere (half-sphere) enclosed inside the unitsphere x2 + y2 +
z2 = 1 and above the z = 0 plane.
1
Problem 3. Consider the solid E bounded by the planes z + y = 1
and x = 1 in the first octant (x, y, z 0).(a) [1 pt] Sketch the
solid E on a Cartesian coordinate system. Be sure to label your
axes.(b) [2 pts] Set up the bounds for the integral
E f(x, y, z) dz dy dx (note the order of integration!).
(c) [2 pts] Set up the bounds for the integralE f(x, y, z) dx dy
dz (note the order of integration!).
BONUS [1 pt] Lets have a midterm review session! Mark with a X
when you are available and number yourpreferred times, with 1 being
the most desirable.
