Let the region R be the triangle with vertices (1, 1), (1,3), (2, 2). Write the...
Q3. If R is the triangle with vertices (2,0), (6,4) and (1,4), then draw the region R' after applying the transformation x = (u – v), y =(u + 40). Also, write the limit for integration in both region, i.e. Ne f(x,y) dA = write the limit for x,y and then covert the integration with limit in R' ?
CHANGING COORDINATES/BASIS Question 1. Let R be the triangle in R2 with vertices at (0,0), (-1,1), and (1,1). Consider the following integral: 4(x y)e- dA. R Choose a substitution to new coordinates u and v that will simplify this integrand. Draw a sketch of both the region R and the image of the region in the u,v-plane. Evaluate the integral in the new coordinate system. Warning: No matter what strategy you use for this integral, it will require at least...
Thanks In evaluating a double integral over a region D, a sum of iterated integrals was obtained as follows: 0 f(x, y)dy dr f (r, y)dy d f(x, y) dA -2 2 TJ= Sketch the region and express the double integral integration as an iterated integral with reversed order of
2. Let f(x,y) = e In(y) and let R be the region in the first quadrant of the plane that lies above r = = In(y) from y=1 to y = 2. (a) Sketch the region R in the plane. (b) Evaluate SSR f(x,y) dA.
Suppose R is the shaded region in the figure, and f(x,y) is a continuous function on R. Find the limits of integration for the following iterated integrals. BD (a) [f $12,9)da = S, "Lº f12, y) dy de PH dA= JE JG f(x,y) dc dy I
6AHW7: Problem 5 Prev Up Next (1 pt) Suppose R is the shaded region in the figure, and f(x,y) is a continuous function on R. Find the limits of integration for the following iterated integrals. Bp D -» [f(3, 3)dA = SL" $12, 9) dy de x,y) dA= f(x,y) dy dx ЈА Јc so || 13 wyda= [." 15:19) de dry We were unable to transcribe this image
ST sy +27*dylv Sketch the region R of integration and write as in iterated integral in the order dxdy. Do not evaluate the integral.
(1 point) Let T'be the region inside the triangle with vertices (0, 0), (3, 0) and (3, 2), and let f(x, y) be the function which is 0 outside of T and f(x, y)-38 SK y Ior (x, y) inside T. 3888 Then E(XY)- 4.8
Calculate the following double integrals. Be sure to include a sketch of the region R. 1. . (2x + 3y)dxdy given R={(x,y)|0 SX < 2,1 sy s3} 2. SR (2xy)dydx given R={(x,y)|0 SX S1,x Sy s 1}
1) The region of integration of I is represented by the blue region in: O a Oc. Od 2) By reversing the order of integration of I, we get: a 1 = $secx dxdy b. I = 8 secx dxdy c. 1 = secx dxdy d. 1 - IL secx dxdy Exercise 6. Double Integral in rectangular coordinates (10 pts 10 pts) Let I= secx dydx. 1) The region of integration of I is represented by the blue region in:...