volumes of revolution a.) Sketch the region in the first and fourth quadrants bounded by the...

volumes of revolution

a.) Sketch the region in the first and fourth quadrants bounded by the graphs of f(x)=x^4-4x^2 and g(x)=4-x^2, and find the area.

b.) find the volume of the solid generated by revolving the region described in part (a) about the line x=-2.

c.) set up, but do not evaluate, the integral which computes the volume of the solid generated by revolving the region described in part (a) about the line y=-2.

d.) set up, but do not evaluate, the integral which computes the volume of the solid having the base described in part (a), whose cross sections perpendicular to the x-axis are semi circles.

Solutions

Expert Solution

The answer is in the pic. If any doubt still remained, let me know in the comment section.

If this solution helped, please don't forget to upvote to encourage us. We need your support. Thanks ☺☺☺ :)

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

Sketch and find the area of the region bounded by the curves ?=?+? and ?=?2−?.

Find the volume of the solid of revolution that is formed by rotating the region bounded...

Find the volume of the solid of revolution that is formed by rotating the region bounded by the graphs of the equations given around the indicated line or axis 1.- y=9-x^2, y=0, around the x axis 2.- y=√x-1, x=5, y=0, around the x=5 3.- y=1-x, x=0, y=0, around the y= -2 4.- y=x^2, x=0, y=3, around the y axis

Recommendations on the fourth industrial revolution,

Sketch the region bounded above the curve of y=(x^2) - 6, below y = x, and...

Sketch the region bounded above the curve of y=(x^2) - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integrals and evaluate the integral.

is africa ready for the fourth industrial revolution

Let R be the two-dimensional region in the first quadrant of the xy- plane bounded by...

Let R be the two-dimensional region in the first quadrant of the xy- plane bounded by the lines y = x and y = 3x, and by the hyperbolas xy = 1 and xy = 3. Let (x,y) = g(u,v) be the two-dimensional transformation of the first quadrant defined by x = u/v, y = v. a) Compute the inverse transformation g−1. b) Draw the region R in the xy-plane and the region g−1(R) in the uv-plane c) Use the...

⃗ Find the volume of the solid of revolution obtained by revolving the planeregion bounded by...

⃗ Find the volume of the solid of revolution obtained by revolving the planeregion bounded by ? = ? − ?² , ? = 0 about line ? = 2 . Mathematics Civil Engineering Please solve this question in 15 minutes is necessary

(1 point) The region in the first quadrant bounded by y=4x2 , 2x+y=6, and the y-axis...

(1 point) The region in the first quadrant bounded by y=4x2 , 2x+y=6, and the y-axis is rotated about the line x=−2. The volume of the resulting solid is: ____

Sketch the region of continuity for f (x; y) on a set of axes and sketch...

Sketch the region of continuity for f (x; y) on a set of axes and sketch the region of continuity for df/dy (x. y) on a separate set of axes. Apply Picard’s Theorem to determine whether the solution exists and whether it is unique. a) y' = 2x2y + 3xy2 ; y(1) = 2 b) y' = sqrt(2x - 3y) ; y(3) = 2

Answer the following questions: Part A: Volumes of Revolution a) Find the volume of the solid...

Answer the following questions: Part A: Volumes of Revolution a) Find the volume of the solid obtained when the region bounded by y = 1/x , and the lines x = 1, x = 3 and y = 0 is rotated about the x-axis. b) Find the volume of the solid obtained by revolving the region bounded by the parabolas y = x^2 and y^2 = 8x about the x-axis. c) Find the volume of the solid obtained by revolving...

Subjects