Real Analysis II
Topic: Iterated integrals
Real Analysis II Topic: Iterated integrals Find the volume of Find the volume of
NOTE: in spherical coordinates the volume is obtained by the sum of 2 iterated integrals Also, please do your best with the handwriting. Thank you very much :) Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz dy dx 14 x2+ y? dz dy de Part 1 Convert the rectangular coordinate integral to cylindrical coordinates and spherical coordinates and evaluate the simplest iterated integral: 13 x dz...
Q1) Evaluate the double iterated integrals. a) (I ay tips dydis Il troszydy des xpáp,.« II xp áp x6 = x« I,I (P
5. Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order. ∫∫Dy dA, D is bounded by y = x - 20; x = y2 9. Find the volume of the given solid. Bounded by the planes z = x, y = x,x + y = 7 and z = 0 14. Evaluate the double integral. ∫∫D 4y2 da, D = {(x,y) I-1 ≤ y ≤ 1, -y - 2 ≤ x ≤ y}
3. 0/1 points Previous Answers Which of the following iterated integrals can be used to find the volume of the given solid? Select all that apply. p2 sin(6) dp do de (1) 6*I" I "p2sinca) dp do do (2) 65L *since) op de do (3) ["("L*since) op dě do (9) LO" ["[*since) op op de Jo J2 (2) (3)
Please show full solutions so i can understand 3. (i) 3pl Set up iterated integrals for both orders of integration forev dA, where D is the region in the ry-plane bounded by y -,4, and z-0 (ii) [3p] Evaluate the double integral in part (i) of this question using the easier order of integration. (ii) [3pl Find the average of the function f(, y) yey over the region D. 3. (i) 3pl Set up iterated integrals for both orders of...
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.
Use polar coordinates to find an iterated integral that represents the volume, V, of the solid described, and then find the volume of the solid.
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
4. Let E be the region in the first octant of R3 contained in the sphere. (a) Formulate the triple integral JJ JBzdV JJJE zdrdydz in spheri iterated integrals ca coordinates as three hi Formulate the triple integral in cylindrical coordinates as three iterated integrals c) Formulate the triple integral in Cartesian coordinates as three iterated integrals 4. Let E be the region in the first octant of R3 contained in the sphere. (a) Formulate the triple integral JJ JBzdV...
4. Use an appropriate iterated integral and coordinate system to find the volume of the solid. B) inside the graphs r-2 cos θ and r. 4 4. Use an appropriate iterated integral and coordinate system to find the volume of the solid. B) inside the graphs r-2 cos θ and r. 4