f(x,y)= x^4 + 2x^2 y^2 + y^4
Double integral
D= (r, theta)
3<=r <= 4
pi / 3 <= theta <= pi
Evaluate double integral over polar rectangular region
3367 pi / 18 is final answer
f(x,y)= x^4 + 2x^2 y^2 + y^4 Double integral D= (r, theta) 3<=r <= 4 pi...
Set up and evaluate the double integral using polar coordinates f(x,y) = 8-y; R is the region enclosed by the circles with polar equations r=cos(theta) and r=3cos(theta). I am struggling with understanding how to determine the interval for theta. The answer key says 0<= theta <= pi but I don't understand why. Please elaborate on this when solving.
Evaluate the double integral of f(x, y) = x + y over the region R bounded by the graphs of x = 14, y = 4, y = 8, and y = 3x-1. Answer: Next page
Evaluate the double integral of f (, y) = x + y over the region R bounded by the graphs of x = 15, y = 4, y = 6, and y = 4x-1.
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
Evaluate the double integral || f(x, y) dA over the region D. JU f(x, y) = 6x + 9y and D = {(x, y)SXS 1, x3 sy s x3 + 1}
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.
6. Use the additivity of the double integral to evaluate the double integral of f(x,y) = x2-y2 over the region that is a disk x2 + y2 < 4 with a triangular hole with vertices (0,0), (0,1), and (1,1).
Evaluate the double integral off (x, y) = x + y over the region R bounded by the graphs of x = 13, y = 2, y = 8, and y = 3x-1. Answer:
Evaluate the double integral for the function f(x,y) and the given first quadrant region R. (Give your answer correct to 3 decimal places.) f(x, y) = 7xe_V'; R is bounded by x = 0, y = x2, and y = 6
(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...