Saturday

December 20, 2014

December 20, 2014

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

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 11:22pmarea = 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 11:48pmor

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 2:42amOh! 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 - What is the connection between improper integrals, Riemann sums, and ...

College Calculus - Could someone explain how to distinguish improper integrals ...

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 - Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if ...

Calculus Area between curves - Consider the area between the graphs x+6y=8 and x...