1

In Exercises 71–76, find the area of the surface generated by revolving the curve about each given axis. $$ x=a \cos ^{3} \theta, \quad y=a \sin ^{3} \theta, \q...

Question

In Exercises 71–76, find the area of the surface generated by revolving the curve about each given axis. $$ x=a \cos ^{3} \theta, \quad y=a \sin ^{3} \theta, \quad 0 \leq \theta \leq \pi, \quad x $$

In Exercises 71–76, find the area of the surface generated by revolving the curve about each given axis. $$ x=a \cos ^{3} \theta, \quad y=a \sin ^{3} \theta, \quad 0 \leq \theta \leq \pi, \quad x $$



Answers

Find the exact area of the surface obtained by rotating the ginve curve about the $ x $-axis.

$ x = a \cos^3 \theta $, $ \quad y = a\sin^3 \theta $, $ \quad 0 \leqslant \theta \leqslant \pi/2 $


Similar Solved Questions

5 answers
2 Eeton conlnehe fonnk ao0 (K, 1Z 410 wina Ltu pH ol this ~Cton baforu unyuddilion ol NiOhT3,74) Thi tcuutondrulidcrln ? taonWhalIne pHi ol Ina solution atur acdition 50,0mL Njoh?Wuhaiyole HOBN Icquiroomach Ina douilcu pointtWhat Kd e4 the equivalence poinn?Ena s taehobs hal clihe fnk ecid has bcen converted fonate?balb dte Atia &ddrion &l 125.0 ML Neor?
2 Eeton conlnehe fonnk ao0 (K, 1Z 410 wina Ltu pH ol this ~Cton baforu unyuddilion ol NiOhT 3,74) Thi tcuuton drulidcrln ? taon Whal Ine pHi ol Ina solution atur acdition 50,0mL Njoh? Wuhaiyole HOBN Icquiroo mach Ina douilcu pointt What Kd e4 the equivalence poinn? Ena s taehobs hal clihe fnk ecid h...
5 answers
Nroron moveswirhveloclty of v (6i _ Sj + k) m/sreglonwhlch the maqnetlc fleld(i + 2jWhat the magnltudethe magnetlc forceDarticie 'xderiencesCheck Your evaluatior of thie cruss pruduct as thislikely source of erorYour caltulalionNeed Help?eteniaEacn
nroron moveswirh veloclty of v (6i _ Sj + k) m/s reglon whlch the maqnetlc fleld (i + 2j What the magnltude the magnetlc force Darticie 'xderiences Check Your evaluatior of thie cruss pruduct as this likely source of eror Your caltulalion Need Help? etenia Eacn...
5 answers
Chapter 30 Problem 041 circular coil has 12.4 cm radius and consists of 25_ closely wouna curns of wire. An externally produced magnetic field of magnitude 3.19 mT perpendicular to the coil, (a} If no current in the coil, what magnetic flux links its tums? (b) When the current in the coil .92 certain direction_ the net flux through the coil is found t0 vanish: What the Inductance of the coil?
Chapter 30 Problem 041 circular coil has 12.4 cm radius and consists of 25_ closely wouna curns of wire. An externally produced magnetic field of magnitude 3.19 mT perpendicular to the coil, (a} If no current in the coil, what magnetic flux links its tums? (b) When the current in the coil .92 certai...
5 answers
We can improve our results by using smaller increments of dx. For the next calculation, use dx = 0.00025 m_ Remember that the charge contained in 0.00025 meters is less than that contained in 0.0OO5 m_RESULTSList your results for the electric fields determined for each trial. 3.53E01 E (dx = 0.OOOSm) N/c 3.54E01 E (dx = 0.00025m) N/c
We can improve our results by using smaller increments of dx. For the next calculation, use dx = 0.00025 m_ Remember that the charge contained in 0.00025 meters is less than that contained in 0.0OO5 m_ RESULTS List your results for the electric fields determined for each trial. 3.53E01 E (dx = 0.OOO...
5 answers
Question 4 Not yet answered Marked out of 7Remove flagA disk of radius r= 70 cm has a uniform surface charge density 6= 60.7 nC Calculate the electric field in units of kNJC) at point P that lies along the central perpendicular axis of the disk and a distance 30 cm from the center of the disk: use ke 9x109 N.m2/c2Select one: A. 2.08B. 4.51C.1.35D. 4.16OE: 1.04
Question 4 Not yet answered Marked out of 7 Remove flag A disk of radius r= 70 cm has a uniform surface charge density 6= 60.7 nC Calculate the electric field in units of kNJC) at point P that lies along the central perpendicular axis of the disk and a distance 30 cm from the center of the disk: use...
5 answers
8.3.64Find the volume of the solid generated when the region bounded by the graph = ofy = sin x and the X-axis o the interval [ - 1, x] is revolved about the X-axis: The described volume is cubic units (Type an exact answer; using T as needed )
8.3.64 Find the volume of the solid generated when the region bounded by the graph = ofy = sin x and the X-axis o the interval [ - 1, x] is revolved about the X-axis: The described volume is cubic units (Type an exact answer; using T as needed )...
5 answers
Diagrar shows circle Mith center 0 and OA, OB are radii: (Angle 2 in radians]Which Nis 19If the radius is (N S) cm; then find the Length of the arc ABIf the radius Is 20 cm,then find the Area of the sector OAB;
Diagrar shows circle Mith center 0 and OA, OB are radii: (Angle 2 in radians] Which Nis 19 If the radius is (N S) cm; then find the Length of the arc AB If the radius Is 20 cm,then find the Area of the sector OAB;...
1 answers
In Problems 1-16, evaluate each indefinite integral by making the given substitution. $$ \int x \cos \left(x^{2}-1\right) d x \text { , with } u=x^{2}-1 $$
In Problems 1-16, evaluate each indefinite integral by making the given substitution. $$ \int x \cos \left(x^{2}-1\right) d x \text { , with } u=x^{2}-1 $$...
5 answers
Find tho volume of revolutlon about the x axis for the given function and Intenvalf(x) =3x - x2[0, 3](A)50 37 n 3 81 10 310 "9 10(B)(C)(D)(E)(F)
Find tho volume of revolutlon about the x axis for the given function and Intenval f(x) =3x - x2 [0, 3] (A) 50 37 n 3 81 10 310 "9 10 (B) (C) (D) (E) (F)...
5 answers
Let flx; Y, 2) = In (xy) + ln (yz) In (xz) be a function and let Po (1, 1, 1) be a given point: Find the direction in which the given function increases most rapidly at Po_ Then find the rate of change of the function in this direction.
Let flx; Y, 2) = In (xy) + ln (yz) In (xz) be a function and let Po (1, 1, 1) be a given point: Find the direction in which the given function increases most rapidly at Po_ Then find the rate of change of the function in this direction....
5 answers
The image formed by a spherical mirror is located at a distance Iql = 6 cm: The lateral magnification is M = +2. What is the radius of curvature; R, of the mirror?0 -12 cm0 +6 cm0 -24 cm0 +12 cm0 -6 cm
The image formed by a spherical mirror is located at a distance Iql = 6 cm: The lateral magnification is M = +2. What is the radius of curvature; R, of the mirror? 0 -12 cm 0 +6 cm 0 -24 cm 0 +12 cm 0 -6 cm...
5 answers
Liven flz,9) = Zx' + 619" _ 3y7 +Jly)fnd nwnlrca| Value of f(5,2) k Find the fllow*J Jtwlial expre sion for #e parta] oeviwhis,
liven flz,9) = Zx' + 619" _ 3y7 +Jly) fnd nwnlrca| Value of f(5,2) k Find the fllow*J Jtwlial expre sion for #e parta] oeviwhis,...

-- 0.025590--