Instructions: Show all your work for FULL credit. Calculators are NOL final answer. Neatness is highly appreciated. 1. A region R, bounded by y 2x, y 6-x, and x-axis, is rotated around the y-axis. Sketch the region R, in the box a) 15 strip/slice you will use to find the volume of the solid of revolution. b) Write the definite integral that gives a X the volume of the solid of revolution. (DO NOT evaluate the integral.) Find the circumference...
l. If the curve y = e-2 sin x, x 0 is rotated about the x-axis, the resulting solid looks like an infinite decreasing string of beads. a) Sketch the first few beads of the solid of revolution, marking where the beads intersect the X-axis. b) Find the exact volume of the nth bead. Show all integration steps c) Write the total volume of the beads as an infinite series and evaluate the series l. If the curve y =...
The region bounded by x = 25 + y x = 0, y = 5, and y = 10 is rotated about the x-axis. Find the volume of the solid of revolution Use your calculator or computer to find the answer rounded to 4 decimal places. Preview The region bounded by x = 25 + y x = 0, y = 5, and y = 10 is rotated about the x-axis. Find the volume of the solid of revolution Use...
The region bounded by f(x)=−2sin(x) x=π, x=2π, and y=0 is rotated about the y-axis. Find the volume of the solid of revolution.
7. Evaluate the following integral. b) SO3(2-1)05 dz c) f (xl dx (15 marks) 8. A shaded region S is bounded by the curve y = the x-axis, the vertical lines x = 1 and x = V2. The x(4-2)1/4 region is rotated through 21 radians about x-axis to form a solid of revolution. Compute the exact volume of the solid of revolution formed. (10 marks) 9. Between the two towers of a suspension bridge that are 2 kilometres apart,...
The region enclosed by y = Vx and y = 5x is rotated around the x-axis. Choose the integral that can be used to find the volume of the solid of revolution. & S (x - 12 ) dx = [" (432 – y") dy
arcsin x dx Hint: Use integration by parts. 2. Find the arc length of the portion of the parabola y = 10x - x that is above the x-axis. Find the volume of the solid of revolution if the region between the curves 3. 4. y = x and y = 4x is rotated about the x-axis. Find the area under the curve defined by the experimental data below by using Simpson's rule. MAT2691/101/3/2019 5. Simplify 3 -2 7 4...
Let C be the portion of the curve rve y = x3 + 3x – 1 between the points (1, 3) and (2, 13). (a) Write down a definite integral for the arclength of C. Do not evaluate the integral. (b) Write down a definite integral for the surface area of the surface of revolution obtained by revolving Cabout the x-axis. Do not evaluate the integral. (c) Write down a definite integral for the surface area of the surface of...
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work) 17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and z-axes respectively, then rotated another 30° about the a-axis. Find the new location (10 marks) and orientation of the frame. 0 0 -1 3 -1 0 0 4 1. a A frame B is rotated 60° about the y-axis, 45° about the n-axis, then translated 4 and 6 units relative to the x- and...