Sin(x) 30. The volume obtained when the area between the sin(x) x-axis for x21 and the graph of f...
The region between the graph of f(x) = 1 In x and the x-axis, for x > 1, is revolved about the x-axis. Calculate the volume of the solid that is created. Hint: Use the Disk Method, and since * goes to the integral will be improper and you will have to use L'Hopital's Rule as part of the calculation
1. The area between the part of the curve-6x 8 above the x-axis and the x-axis itself is 2. The area below y 4x -x and above y 3 (for1 xS 3) is revolved around the x-axis. 3. The areas between the following portions of curves and the x-axis are revolved around the revolved by an angle 2π around the x-axis. Find the volume swept out. Find the volume swept out. y-axis. Find the volume swept out. (a) y- betweenx...
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of the region bounded by one arch of the graph f and the x -axis. b) Find the area of the triangle formed by the x -axis and the tangents to one arch nts to one arch of f at the points where the graph of f crosses the x -axis
Let f(x) k sin(kx), where k is a positive constant (a) Find the area of...
(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...
1. A, on a coordinate axis (1)sketch x? + (y – 5)2 = 9, (2)describe the graph, (3)the graph is revolved about the x-axis, set-up integral which will compute its VOLUME, simplify the integrand as much as possible but DO NOT DO THE INTEGRATION. B. The triangle whose vertices are (0,0), (2,8) and (2,2) is revolved around the (a)x-axis, (b)y-axis (1)find the eqs. Of the sides, (2)draw graph, (3)compute (a) and (b) C. A student on test was asked to...
The region between y=x and y=(x-2)^2 is revolved about the x axis. Find the volume of the solid. Then find the volume if revolved about the y-axis.
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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+...
11. (20 points) Compute the volume obtained by rotating the area between the s-axis and the graph of for 0 SS2 around the y-axis. (Give the exact answer, no rounding!) () +1
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].
Find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval [-21/3, 31/4]. The area is (Type an exact answer, using radicals as needed.)