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• ### 1) Find the volume of the solid obtained by rotating the region in the first quadrant...

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.

• ### 2) The region R in the first quadrant of the xy-plane is bounded by the curves...

2) The region R in the first quadrant of the xy-plane is bounded by the curves y=−3x^2+21x+54, x=0 and y=0. A solid S is formed by rotating R about the y-axis: the (exact) volume of S is = 3) The region R in the first quadrant of the xy-plane is bounded by the curves y=−2sin(x), x=π, x=2π and y=0. A solid S is formed by rotating R about the y-axis: the volume of S is = 4) The region bounded...

• ### The region bounded by f(x)=−2sin(x) x=π, x=2π, and y=0 is rotated about the y-axis. Find the...

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.

• ### 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 d...

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...

• ### Define R as the region that is bounded by the graph of the function f(X)=x^3/6+2, the...

Define R as the region that is bounded by the graph of the function f(X)=x^3/6+2, the xaxis, x=-1, and x=1. QUESTION 9 · 1 POINT 23 Define R as the region that is bounded by the graph of the function f(2) +2, the x-axis, x = -1, and x = 1. Use 6 the disk method to find the volume of the solid of revolution when R is rotated around the z-axis. Submit an exact answer in terms of ....

• ### 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. Sk...

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...

• ### all answer 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...

all answer 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+...

• ### Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis....

Math232 2 Consider the region in first quadrant area bounded by y x,x=6, and the x-axis. Revolve this bounded region about the x-axis a) Sketch this region and find the volume of the solid of revolution; use the disk method, and show an element of the volume. (15 marks) b) Find the coordinates of the centroid of the solid of revolution Find the moment of inertia of the solid of revolution with respect to the x-axis. d) Math232 2 Consider...

• ### 8. Consider the region bounded by the y = x2 - 2x + 1 and y...

8. Consider the region bounded by the y = x2 - 2x + 1 and y = 1 + 2x - x? Find the area of the region. a. b. Find the volume of the solid when the region is rotated about the x-axis. c. Find the volume of the solid when the region is rotated about the y-axis. d. Find the volume of the solid when the region is rotated about the line x = 5. e. If the...

• ### Find the volume of the solid obtained when the region bounded by the y- axisthe region bounded byy- 3a2- andy-0 is...

Find the volume of the solid obtained when the region bounded by the y- axisthe region bounded byy- 3a2- andy-0 is rotated about the y - axis. Find the volume of the solid obtained when the region bounded by the y- axisthe region bounded byy- 3a2- andy-0 is rotated about the y - axis.