Anonymous
Anonymous asked in Science & MathematicsMathematics · 7 years ago

Calculus one volumes of solids of revolutions questions?

Hi, I am preparing for a test and I have a few questions for which I do not have the answer to that I would like to compare. Thank you in advance for the help!

1) Set up, but do not evaluate the following integrals, which will solve for volume

a) y= 5-x^2 and y=4x, rotated around line y=8

b) y= 5-x^2 and y=4x, rotated around line y=-30

c) y= 5-x^2 and y=4x, rotated around line x=7

d) y= 5-x^2 and y=4x, rotated around line x=-10

2) Find the volume obtained as the region bounded by y=tan(x), x=pi/6, x=pi/4 is rotated around x-axis.

3)Find the volume obtained as the region bounded by y=x and y=x^2 is rotated around x-axis.

4)Find the volume obtained as the region bounded by y=sqrt(x-3), x=4, x=7, y=0 is rotated around the y-axis.

5)Set up, but do not evaluate the following integrals which will give surface area.

a) x=10-y^2 and the y-axis, is rotated around y=5.

b) x=10-y^2 and the y-axis, is rotated around x=11.

c) y=sin(pix/4) on [4,8] is rotated around the line y=4pi

d) y=sin(pix/4) on [4,8] is rotated around the line y=-4pi

6) Find the exact arc length of:

a) y= 3/8(x^4/3-2x^2/3) on [1,8]

b) 24xy=y^4+48 between y=2 and y=4.

7)The base of a solid is a circular disk with diameter 10. Find the volume if each cross-section is a square.

8)Prove the formula for surface area of a sphere by considering the semi circle y= sqrt(r^2-x^2) rotated around x-axis

1 Answer

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  • Anonymous
    7 years ago
    Favorite Answer

    1/

    a/ the x-intersect between 2 graphs , x^2+4x-5=0--->x = -5 or 1

    V = pi { integral of [(4x)^2 - (5-x^2)^2] dx , from x=-5 to x=1 }

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