Monday

January 26, 2015

January 26, 2015

Posted by **Anonymous** on Friday, November 23, 2012 at 3:03pm.

a) Compute the perimeter P and area A of R, and then compute the ratio Q = A/P2.

Note By squaring the perimeter the ratio becomes independent of the units chosen to measure the region.

b) Compute this ratio Q = A/P 2 for these four regions: the region R, a square, a circle, and an equilateral triangle. Draw the figures in increasing order of Q.

- calculus II -
**Reiny**, Friday, November 23, 2012 at 6:00pmI assume you know the formula for the length of a curve in Calculus.

L = ∫( 1 + (dy/dx)^2 )^(1/2) dx (from left x to right x)

This is the hard part of the question

I ended up finding the length of the parabolic curve to be

L = 2∫(1 + 4x^2)^(1/2) dx from x=0 to x=2

I ran this through WolFram to get

http://integrals.wolfram.com/index.jsp?expr=%281%2B+4x%5E2%29%5E%281%2F2%29&random=false

sub in the values, add on the distance from (-2,4) to (2,4) and you have the perimeter of R

For the area:

A = 2∫(4 - x^2) dx from x = 0 to 2

which you should be able to do quite easily.

The length of the curve is the only difficult part of the problem.

**Answer this Question**

**Related Questions**

Calculus - please help! - Suppose that 0 < c < ¥ð/2. For what value of c ...

Calculus - Express the area of the region in the xy-plane enclosed by the curve...

pre-calc - area of a rectangular region: a farmer wishes to create two ...

calculus - Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...

calculus - the region enclosed by 2y=5xy=5 and 2y+3x=8. Decide whether to ...

Calculus - Sketch the region enclosed by the given curves. Decide whether to ...

Calculus - MathMate Please help - I asked this question on last thursday and u ...

calculus -- PLEASE HELP! - Suppose you are trying to evaluate the intergral 2x^...

Calculus 2 - Sketch the region enclosed by y=e^2x, y=e^6x, and x=1. Decide ...

calculus - Sketch the region enclosed by x+y^2=42 and x+y=0. Decide whether to ...