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
A flat plate has an area D specified by the constraints y> 0 and 1 < x2 + y2 <16. If the density is given by p(x, y) = y y (22 +32) then the mass of the plate is given by the double integral SJ p(,y) dedy D Evaluate the double integral using polar coordinates z=r cos (O) and y=r sin (O). SJ p(x,y) d.ody= D Preferably leave you answer in terms of fractions, exponentials or 7. If you...
Find the volume of the solid obtained by rotating the region bounded by y=r", y=0, x=1 about the y-axis. (a) ('(1 – VD? dy # [12 – (3y)?] dy (e) [ a[(79+1)2 – 1º) dy
= r.Cos (0), y r sin(0), and zr0 Let x.y,z)=x y+y zxz, where x 3-where w(r,0) = u(x(r,0),y(r,0),2(r,0)) Owr.0) for r= 1, 0 = д0 (r,0) and дr Evaluate 2
= r.Cos (0), y r sin(0), and zr0 Let x.y,z)=x y+y zxz, where x 3-where w(r,0) = u(x(r,0),y(r,0),2(r,0)) Owr.0) for r= 1, 0 = д0 (r,0) and дr Evaluate 2
Given that yı(x) = r-1 is a solution of 2c?y" + 3ry - y=0. Find a second solution of the given equation by using the method of reduction of order. O y2(:-) = O 42(:) = 1-1/2 O 42(x)=1/2 O y2(x) = 73/2 Oy2(r) =
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
Find the centroid of the infinite lamina with > 1 and 0 <y<r-3 with density 8(x, y) = 1.
the DE 3xy', + (2-x)y'-y-0 and when r-0 С.-Cu-1. When r-1. ck-Ser. For Find two power series solutions to the DE. (points 10) 3 k 1,2,3, both k
the DE 3xy', + (2-x)y'-y-0 and when r-0 С.-Cu-1. When r-1. ck-Ser. For Find two power series solutions to the DE. (points 10) 3 k 1,2,3, both k
Question 5 +(-12) and y= la. We assume that the density of We want to compute the centre- f mass (or centroid) of the region enclosed by the curves y this flat regian is constant. a) Find the -coordinate of the points of intersection of these two curves. List your values separated by semicolons. 1 point How Did I Do? Answer: of the region R. b) Find the area A=Number c) Find the moment My of the region R about...
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.
1. Use polar coordinates to evaluate the double integral dA z2 +y where R is the region in the first quadrant bounded by the graphs x = 0, y = 1, y=4, and y V3z.