Posted by **Alyssa** on Saturday, October 2, 2010 at 9:32pm.

Find the area of the curve y = 1/(x^3) from x = 1 to x = t and evaluate it for t = 10, 100, and 1000. Then find the the total area under this curve for x ≥ 1.

I'm not sure how to do the last part of question ("find the the total area under this curve for x ≥ 1.")

For the area of the curve, I found that the integral from 1 to t is (1/2)-[1/(2t^2)].

I used the equation I found and substituted t for 10, 100, and 1000, and got 0.495, 0.49995, and 0.4999995 respectively.

- Calculus ll - Improper Integrals -
**Reiny**, Saturday, October 2, 2010 at 11:22pm
area = LIM [integral]1/x^3 dx from x = 1 to x -- infin.

= lim (-(1/2)(1/x^2) from x=1 to x-- inf.

= lim{ -(1/2)/x^2 as x--inf} - lim {(-1/2)/x^2 as x=1

= 0 - (-1/2) = 1/2

- Calculus ll - Improper Integrals -
**Reiny**, Saturday, October 2, 2010 at 11:48pm
or

look at your expression of

1/2 - 1/(2t^2)

as t ---> infinity, doesn't 1/(2t^2) approach 0 ?

so you are left with 1/2 -0

= 1/2 , as your approximations suggested.

- Calculus ll - Improper Integrals -
**Alyssa**, Sunday, October 3, 2010 at 2:42am
Oh! I understand now. The "total area" part kind of threw me off.

Thank you so much!

## Answer This Question

## Related Questions

- Calculus - Integrals: When we solve for area under a curve, we must consider ...
- MATH - Evaluate by writing it as a sum of two integrals and interpreting one of ...
- calculus - how would you do this improper integral 1/(x-1) from 0 to 2 this is ...
- calculus - how would you do this improper integral 1/(x-1) from 0 to 2 this is ...
- Calculus - Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if ...
- math, calculus 2 - Consider the area between the graphs x+y=16 and x+4= (y^2). ...
- calculus showed work - find the area of the rgion bounded by the graphs of y=x^3...
- calculus II - We're doing areas by integrals now, with 2 eqns. I have a few ...
- Calculus - What is the connection between improper integrals, Riemann sums, and ...
- math, calculus - 1. Consider the region bounded by the curves y=|x^2+x-12|, x=-5...

More Related Questions