Section 15.1: MATH320_001 FA2020 co The Fremennik Trials – OSRS WIKI so Quest experience rewards – OSRS Wiki 3 Course (a) Use a Riemann sum with m – 3, n-2, and take the sample point to be the upper right corner of each square. 324 x (b) Use the Midpoint Rule to estimate the volume of the solid. (No Response) Estimate the volume of the solid that lies below the surface z = xy and above the following rectangle. R:= {(x,x)1654s 12,0 s y s4} (a) Use a Riemann sum with m – 3, n = 2, and take the sample point to be the upper right corner of each square. 324 x (b) Use the Midpoint Rule to estimate the volume of the solid. Need Help? Read it Watch It Master it Submit Answer [-/1 Points] DETAILS SCALC8 15.1.011. Evaluate the double integral by first identifying it as the volume of a solid.

## Answer

(@) AX = 12-6 – 2 (3=24 | (8,4) (1994) (254) splacing along X-asis: (3=112 Spacing along to aus: 3ym (8,2092) (122) 8 6 iso 10 i-2 12 – 3 4-0 AY= – 2 zyn . The elementary area of the base of solid in xy-plane is AA = AR. AY Here Z=XY i. The value of Z at the upper right corner of each square are : j (74’s Yoj) Zij= Xi Yj (82) 16 Ć 1 2 32 2 1 (84) (1012) (1024) 20 2 40 3 ? (12,2) 24 2 (12,42 48 .: Reqd Reimann sur ZFzij=180 = ŽŽ ZA+ & & Zij 14 il J=1 isl yal 3 즐을 4 2 Zij is 1 j=1 : 4x 180 – [729] (Reza)

Yz 4 (73) 697) (113 3 Y, 2 (7011 (11 1 AX=2 { for all i,i) 7 8 9 10 11 12 4ษ 70 4 개 x2 전 X3 AA 4 z(711) = T z (7,3) = 21 z (911) = Z (9,3) = 27 7 (11)’) = 11 2 (113) = 33 Using Mid point rule, estimated volume (7 +21+9+27+11+33) *4 108x 432 Read) &