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Math 53 Quiz 7 Name:
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.
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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.
Time Avail. Pref.
Sunday 1-3pm
Monday 8-10pm
Tuesday 8-10pm
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