Question

1. Consider the solid of greatest volume bounded by the graphs of z = 0, 9 - ?- y, and y = 2. i. Clearly sketch the graph of the solid. ii. In how many distinct ways can three distinct objects be ordered? iii. Present all distinct triple integrals in rectangular coordinates that determine the volume of the solid, where the distinction lies solely in the order of integration

Answer 1

ANSWER:

2 Here the graph is given given by 2=0 z2_9.x2-y² x² + y²+2²=9 12=0) 59-x2_yz y=2) 1

9. "y=2 sy fig (1) X figure 6 is the required goraphi (6 of 250, ZEO, Noi distinct ways, thecee ditline objecta can bo ordered is 3! (3x2x1 - 6 How the solid is Sa - 1²-y?, Y=2 Oeze Ja-na-ya Also when x² + y²-9 y? - 9-X2 22 y = 59-x2 and y=59-x2 oul Y=2 012-49-) ² - 5 no [s 032=3 (5 <**3) 59-12 y 2 Volume da dy da < when yoo 59-22 ㅗ x = 15 y = 2 2 60 al Also x2 + y²=9 21= 59-y2 : Y=2, n = lamang 2342 3. (al- * 50 s pq-ya pA -x2 ya 55 52-39-42 d9-42 -x2-y2 ²1 y ² - 1 =) y 29 V- dadady y= 2 = Y-3 250

Also when y=2, x²+y²+ z2zq o xe2+22=5 g=y= Jara?g? ܓ >0- X2+22=5 x= 15-22 (•:270) +2²=5 at n=0 >2=55 (: 280 given x2+2²= rs represents circle in u-2 plane a 55 55 J5-22 59-22_22 dy dadz Z=0 860 55-12 s dy dzda n=0 2-0 y=2 ja -n2_22 Si x²+2²5 represents y=2 a circle with alow finally x² + y2+2²=9 radius is x 59-y?-22 g²+2²=91 in y-2 -2 b leene). z = Ja-ya Asocate ya Os 2459-42 and 2<3 <3 ( y2+22=4 Ja-y2 Sa-y2z2 is a circle of readices when ne=o, w Va da dady y=2 Ž=0 NEO

Also asdsJ9-92_2² 22 +4²+2²=q a y=J9-22 22 y = 59-22 also al-y=2, y²+2?=93) 2²=5 =) 2=15 and at y zo, 2 ſs s2<3 J१-22 J9-4²2² dadydz. 2= rs y=2 233

NOTE:: I hope this answer is helpfull to you......**Please supppoer me with your rating

**Please give me"LIKE".....Its very important for me......THANK YOU