Calculus Check

posted by .

The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3.
Here is what I have so far:
Radius = 1/(x^3)
Area of Cross Section = pi(1/(x^3))^2
Simplified: pi(1/(x^6))
Volume = (definite integral from 1 to 3) pi(1/(x^6)) dx
= pi( -1 / 5(3)^5) - pi(-1 / 5(1)^5)
= pi (-1 / 1215) - pi (-1 / 5)
= pi(242 / 1215) = 0.625732858
Is this right?

Sincerely,
Mooch

  • Calculus Check -

    just right. good job.

  • Calculus Check -

    Thank you. From now on, I will include my work for reference. As you can see, I do know (to a degree) what I am doing. However, my practice instructions aren't always very clear on how to carry out these problems so I look for a second opinion to back me up. Again, thank you.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    let R be the region bounded by the graphs of y = sin(pie times x) and y = x^3 - 4. a) find the area of R b) the horizontal line y = -2 splits the region R into parts. write but do not evaluate an integral expression for the area of …
  2. math

    let R be the region bounded by the graphs of y = sin(pie times x) and y = x^3 - 4. a) find the area of R b) the horizontal line y = -2 splits the region R into parts. write but do not evaluate an integral expression for the area of …
  3. integral Calculus

    The region in the x-y plane bounded by the curve y=x^2, the line x=0 and the line x=5 and the x-axis. find the volume generated. can you help me check for correction the answer i got was = 625 You want to find volume. Are you rotating …
  4. Calculus AP

    Let R be the region bounded by the graphs of y=cos((pi x)/2) and y=x^2-(26/5)x+1. A. Find the area of R. B. The vertical line x=k splits the region R into two equal parts. Write, but do not solve, an equation involving integrals that …
  5. Calculus

    We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
  6. Calculus

    We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
  7. calculus

    The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume of …
  8. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but …
  9. Calculus

    A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid
  10. Calculus

    'Find the volume of the solid generated by revolving the region bounded by x=16-y^2, x-axis, and y-axis around the x-axis.' I know in theory how to do it, but I'm a little confused by what constitutes the bounded region because it's …

More Similar Questions