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Calculus Check

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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.

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