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(1 point) Convert the integral 4/12 16-Y 1=f* pv T x** de dy 2P+8yº do dy...
1. An iterated double integral that is equivalent to *** dx + ry dy JOR 3. Use Groen's Theorem to set up an iterated double integral equal to the line integral $+eva) dx +(2+ + cow y) dy where is the boundary of the region enclosed by the parabolas y rand 1 = y2 with positive orientation. This yields: A. where R is the triangular region with vertices (0,0),(1,0) and (0,1) is: A B. B. So ['(2-z) dr de SL...
The path integral of a function f(x, y) along a path e in the xy-plane with respect to a parameter r is given by 2. fex,y)ds= f(x),ye) /x(mF +y(t" dr , where a sr sb. (a) Show that the path integral of f(x, y) along a path c(0) in polar coordinates where r=r(0), α<θ<β, is Sf(r cos 0,rsin e) oN+( de. (b) Use this formula to compute the arc length of the path r 1+cos0, 0<0 27 The path integral...
solve problem 6 it is not a double integral, it is 1 integral In Convert to cylindrical coordinates ſyddy Set up the integral) 1b. Convert to spherical coordinates JJ Jy daddy (Set up the integral) 2. Une cylindrical coordinates to determine the volume of the solid in the 1" octant enclosed by the coordinate planes, the cylinder + 16 and the plane (Set up - do not solve) 3. Use spherical coordinates to determine the volume of the solid that...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
dy a. Set up an integral for solving de 1 when y(0) = 0 22 - 25 y() = + t = b. Evaluate your answer to the previous part to find y(). y(2) = help (formulas) (1 point) Solve y" = sin(x) if y(O) = 0 and y'(0) = 9. y(I) help (formulas)
1. Evaluate the line integral S3x2yz ds, C: x = t, y = t?, z = t3,0 st 51. 2. Evaluate the line integral Scyz dx - xz dy + xy dz , C: x = e', y = e3t, z = e-4,0 st 51. 3. Evaluate SF. dr if F(x,y) = x?i + xyj and r(t) = 2 costi + 2 sin tj, 0 st St. 4. Determine whether F(x,y) = xi + yj is a conservative vector field....
(1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0 (1 point) Evaluate the integral. 16 16- S. 1 (a2y2z2)1/2 dy dz dx 16-r 0
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
6. (4 pts) Consider the double integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a) Sketch the region of integrationRin Figure 3.(b) By completing the limits and integrand, set up (without evaluating) the integral in polar coordinates. -1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts) Consider the double integral V2 /2-y² + = (x2 + y) dx dy + + y) do dy. 2-y2 (a) Sketch the region of integration R in Figure 3. (b) By completing the limits and integrand, set up (without evaluating)...
(1 point) Evaluate the line integral ScF. dr, where F(x, y, z) = -4xi – 4yj + 5zk and C is given by the vector function r(t) = (sin t, cost, t), osts 31/2. 4