4. Find the double integr ral ry drdy where D is the unit circle in the...
Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant. P ( − 4 5,
JJD ...... 24. Complete the definition of double integral: Iff: D-R (where DRP is is on D, then S/. 113. y) drdy = iff for all independently of always exists and always has the se In this definition: AD, is (En)E . are is
Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant. Coordinates Quadrant PC :-) IV
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...
3. Let D be the region in the first quadrant lying inside the disk x2 +y2 < 4 and under the line y-v 3 x. Consider the double integral I-( y) dA. a. Write I as an iterated integral in the order drdy. b. Write I as an iterated integral in the order dydx c. Write I as an iterated integral in polar coordinates. d. Evaluate I
14 only
13. Use double integrals to find the area inside the curve r = 1 +sin 14. (a) Express f Io ry dy dr as an integral over the triangle D, which is the set of (u. v) where 0s u s 1, 0 ssu (HINT: Find a one-to-one mapping T of D onto the glven region of integration.) (b) Evaluate this integral directly and as an integral over D* 15. Integrate ze+ over the cylinder
13. Use double...
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.
F(x,y) =<2xy,x^2+y^2> the part of the unit circle in the
first quadrant oriented counter clockwise
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
Question 5. (15 pts) Find the maximum and minimum of f(t,y) = ry? on the circle x2 + y2 = 1
(a) | Sex*+dyds, where D is the circular region inside the unit circle (b) | SF | 13(x2 + y2)dV, where V is bounded by y = 222 +222 and y=8.