1. Calculate the volume of the region bounded by the following two regions in R3: x2...
please answer 1&2
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x", y = 5x, x2 0; about the x-axis V = Sketch the region. y у 5- 6 4 3 3 N -0. 0.5 1.0 X 1.5 -0.5 0.5 1.0 1.5 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 =...
Question 7 (4p) Find the volume of the region bounded above by the sphere x2 + y2 + z2 = 2 and below by the cone z = x2 + y2 and for which x > 0 and y s 0.
[4] Sketch the region bounded above the curve of y = x2 - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integral ans evaluate the integral. -4 -3 -2 -1 0 1 2 3 4 [5] Find the area of the region bounded by the given curves x - 2y + 7 = 0 and y2 -6y - x = 0.
Find the volume of the solid created by revolving the region bounded by the curves y=x2 and x2+y2= 1 about the x-axis.
Find the volume of the solid generated by revolving the region R bounded by the graphs of the given equations about the y-axis. 17)x= x=0, between y=- 4 and y = 4 17) 18) bounded by the circle x2 + y2 = 16, by the line x = 4, and by the line y = 4 18) Find the volume of the solid generated by revolving the region about the given line. 19) The region in the first quadrant bounded...
Class Exercise 2. Find the volume generated by rotating the region bounded by the given curves about the specified line. 4, t y2; x = 4. 2y (b) y sin and y = cos x, on the interval [,]; x = . (c) y = 22, y 0, x -1 , x = 2; y 3/ 3, y = 8, x - y 2; y = -2. 5. (d) x = y (e) y = 2x, y =; y =...
solve parts b,d and f
2. Compute the integral of f over S where (a) f(ayz)xy+z.S is the region in the first octant with xy+ (b) f(xy.z)xxyz, S is the region defined in 2(a) (c) f(x,y.z) x + y2-xz, s is the region bounded by the x'y plane, the plane z (d) f(x,y,z) 2, and the cylinderx2 y z, s is the region in the first octant bounded by r2 + y2 + 2 4 (e) f(xy,z-2, s is the...
Find the volume of the given solid region bounded below by the cone z = \x² + y2 and bounded above by the sphere x2 + y2 + z2 = 8, using triple integrals. (0,0,18) 5) 1 x? +y? +22=8 2-\x?+y? The volume of the solid is (Type an exact answer, using a as needed.)
#2 g and #3&4 please!!!
#2 For each of the following, first sketch (roughly) the region enclosed by the given curves, labelling any important points of intersection, then find the area of the shaded region. WARNING: Make sure that you give a solid attempt and a guess to the graph BEFORE looking at the answers, or you will likely find yourself unable to do these problems on a test! (a)--(-2)2,--- (h) 4x + y2 = 12, *= fety-12-22 - x²6...
1. Find the volume of the solid generated by revolving the region bounded by y = 4x - x and y = x about the x-axis. 2. Calculate the following integrals. r? a. =dx √25-x²