Find the volume of the solid obtained by rotating the area under the graph of y=x2(1-x2)1/2 over the interval (0,1) about the y axis.
Find the volume of the solid obtained by rotating the area under the graph of y=x2(1-x2)1/2...
Find the volume of the solid obtained by rotating the region underneath the graph of f(x) = - about the y-axis over the interval [1, 3].
3. (a) Find the exact volume of the solid obtained by rotating the region between the curves y = - andy (1 – 26) on the interval (0, 1] about the y-axis. (6) Find the center of mass of the region under the graph of f(x) = 1 + x2 + x* on the interval (-1,1).
Problem 2
(1) Find the area enclosed by the curves y 2 and y-4z-z2 (2) Find the volume of the solid whose base is the triangular region with vertices(0, 0), (2, 0), and (0,1). Cross-sections perpendicular to the y-axis semicircles. are (3) Find the volume of the solid by rotating the region bounded by y=1-z2 and y-0 about the r-axis. 2-z2. Find the volume (4) Let R be the region bounded by y--x2 and y of the solid obtained by...
1) Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the curves x=0, y=1, x=y^7, about the line y=1. 2) Find the surface area of revolution about the x-axis of y=7x+4 over the interval 1≤x≤4. 3)The region bounded by f(x)=−1x^2+5x+14 x=0, and y=0 is rotated about the y-axis. Find the volume of the solid of revolution. Find the exact value; write answer without decimals.
1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1.
1. Find the volume of the solid obtained by rotating the region bounded by the following curves about the horizontal line y=-3: y=6-x2,y-2, x = 1.
3. (a) Find the exact volume of the solid obtained by rotating the region between the curves y = = and y = (1 - 26) on the interval [0, 1] about the y-axis. (b) Find the center of mass of the region under the graph of f(x) = 1+z2+z* on the interval (-1,1].
(1 point) Find the volume of the solid obtained by rotating the region in the first quadrant bounded by y=x2, y= 1, and the y-axis about the line y= -2. Volume =
(10 points) 4. Find the volume of the solid obtained by rotating about the x-axis the region between the graph of y = e*, the x-axis, and the lines x 1 x 2 in the first quadrant about the x-axis. Draw a sketch of this solid. 5 3- 2- 1- -4 -1 5 3 0 1 2 5
(10 points) 4. Find the volume of the solid obtained by rotating about the x-axis the region between the graph of y...
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Sample Test 4 1575 Calculus II 1. The region bounded by the parabola y-4x-x and the x -axis is revolved about thex- axis. Find the volume of the solid. Write answer in term of π. Find the area enclosed by the curves: 2. y=2x2-4x-12 y=x2-6x+12 and 3. Find the volume of the solid obtained by rotating the region bounded by the graphs of a. y-x-9, y 0 about the x-axis. -1 about the x-axis. b. y 16-r, y-3x+...
1. Find the area under the graph of y = 1 + x2 over the interval [1, 12] 2. Find: (-) (2x3 - *** -* - x - 1)dx = What can you say about the area between this polynomial and the x-axis over [-1, 1]?