please help Use the disk method to find the volume of the solid generated by rev

Question

please help

Use the disk method to find the volume of the solid generated by revolving the region bounded by y = 2x, y = 0, and x = 5 about the x-axis. The volume of the solid generated is cubic units. (Type an exact answer, using n as needed.) Use the disk method to find the volume of the solid generated by revolving the region bounded by the given line and curve about the x-axis. The volume of the solid is (Type an exact answer, using n as needed.) Use the washer method to find the volume of the solid generated when the region bounded by V = 18x and v = 6x2 is revolved about the x-axis. The volume of the region is (Type an exact answer, using n as needed.)

Explanation / Answer

1) volume = pi* integrate from x1 to x2 (function)^2 dx

=pi* integrate from(0) to 5 ( 2x)^2

=pi *[ 4*(x^3)/3 ]0 to 5

= pi * 500 /3

2)

volume = pi* integrate from x1 to x2 (function)^2 dx

= pi* integrate from x1 to x2 (function)^2 dx

here we should first calculate x1 and x2

x-intercept of the function is calculated by putting y =0

so (36-x^2)^(1/2)=0

x=+6,-6

so

volume= pi* integrate from -6 to +6 ((36-x^2)^(1/2))^2 dx

= pi * integrate from -6 to 6 (36-x^2) dx

= pi * (36x - x^3/3)(-6 to 6)

= 288*pi

3) washer man method states that :

volume = pi * integration a to b ([f(x)]^2-[g(x)]^2) dx

for calculating a we should 1st calculate a and b

so finding the tersection we get

18x= 6x^2
6x^2-18x=0
x=0 and x= 3

a=0 and b=3

volume = pi * integration a to b ([f(x)]^2-[g(x)]^2) dx
finding the tersection we get
18x= 6x^2
6x^2-18x=0
x=0 and x= 3

volume = pi * integration 0 to 3 ([18x]^2-[6x^2]^2) dx
= pi * integration 0 to 3 ([324 *(x^3)/3-[36*(x^5)/5])
= 108*27-36*243/5
= pi *1166.4

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.