Calculus Based On Integration Exam Practice Four question on integration.Kindly make it step solution – either hand written or on word file whichever convenient for you. Find attachment MATH 210 – ASSIGNMENT 2
Due: Friday 04/11/2020 11:59 PM
Before working on this homework, please read the following carefully:
• This homework consists of FOUR (4) problems. Make sure that you
do all of them.
• You are strongly advised to submit this homework two days before
deadline in order to avoid last minute glitches. There will be no extensions granted.
• While submitting, make sure that you assign the solutions to the appropriate problems. There will be no credit for erroneously submitted
solutions.
• This homework will count for 5% of your final grade and you should
try to provide correct, legible and well-written solutions.
The present homework is based on integration in cylindrical and (optionally)
spherical coordinates.
1. Use integration in cylindrical coordinates in order to compute the volume of:
U = {(x, y, z) : 0 ≤ z ≤ 9 − x2 − y 2 }
2. Use integration in cylindrical coordinates in order to compute the volume of:
U = {(x, y, z) : 0 ≤ x2 + y 2 ≤ 1,
0 ≤ z ≤ 7 − x − y}
3. Use integration in cylindrical or spherical coordinates in order to compute the volume of the ball of radius 3 centered at (0, 0, 0).
4th problem on the next page
1
ZZZ
z dV , where U is the part of the ball of
4. Compute the integral
U
radius 2, centered at (0, 0, 0), that lies in the 1st octant. Recall that
the first octant is the part of the 3d space where all three coordinates
x, y, z are nonnegative. (Hint: You may use cylindrical or spherical
coordinates for this computation.)
2
Purchase answer to see full
attachment