17.3 Evaluate the following integral: SSR cosh(x + y)dA where R is the region bounded by...
2. (35pt)Evaluate SS 3xy²dA, where R is the region bounded by the graphs of y = -x and y = x2, x > 0 and the graph of x = = 1. R
Question 3 Evaluate Sſezx=3> 22x+3y dĀ where R is the region bounded by x = 0, y = 0 and x + y =1. (10 marks) R
(1 point) Using polar coordinates, evaluate the integral ST sin(x2 + x>)dA where Ris the region 1 5x2 + y2 549. 1.080
х Evaluate SS arctan arctandA, where the region bounded by x2 + y 21, x² + y2 <4 and O sysx. Select one: a. 16 b. 3л 16 c. 37 8 377 64 3712 32 e
Using a triple integral, calculate the volume of the region in the first octant (x > 0, y 20, z > 0), bounded by the two cylinders z2 + y2 = 4 and c? + y2 = 4.
14) Determine the volume of the solid obtained by rotating the region bounded by y = 4.r and yrr about y-axis. Assume that r> 0.
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
Evaluate the double integral integral | | =+ wy? + rʻydA R where R= {(x,y) 1<x<2,1 <y<2} Double Integral Plot of integrand and Region R 300- 1] 1] 200 1] 100 0 -100 /1) /1) 0/1) 0/1) (0/1) 3/19 ersion -200 -300 101234 This plot is an example of the function over region R. The region and function identified in your problem slightly different Preview Answer Round your answer to four decimal places
using this formula 2. Evaluate the surface integral F. dS, where F(x, y, z) = xi+yj+zk is taken over the paraboloid z=1 – x2 - y2, z > 0. SA errom bove de SS (-P (- Puerto Q + R) dA dy