calculus wxmaxima
posted by jessica .
does anyone know how to approximate the are and circumfrence of the region bounded by the given curves
y=cos(x^2 +(100493/100000)), y=1+xX^2

The two curves intersect at
0.4425 and 1.8018.
By integrating (numerically)
f(x)=cos(x^2 +(100493/100000))  (1+xx^2)
between the two roots, you would get the area as 1.99326.
The perimeter can be obtained by integrating the curve length of the separate curves between the same limits.
See for arclength:
http://en.wikipedia.org/wiki/Arc_length 
For graph of function, see:
http://img20.imageshack.us/i/1297900781.png/ 
Thank you very much but i am still confused with the arc length or the circumference

To find the curve length, we only need to integrate ds (incremental distance) between the given limits.
The expression of ds is basically the slant distance obtained by sqrt(dx²+dy²), so the integral is:
∫sqrt(1+(dy/dx)²dx
It gets a little messy unless the function is a polynomial, but calculating using numerical integration is rather easy, even for complicated functions.
For the cosine part of the function, the derivative should be done using the chain rule, and you should get:
dy/dx = sin(x^2 +(100493/100000)) * 2x
Apply the integral above and integrate from 0.44 to 1.8 (approx.) to get about 3.4 as the arc length.
Check: Δx = 1.8(0.44)=2.24
3.4/2.24=1.5 approx. which is about sec(45°).
If you have other questions, just post. 
i understand but i just don't know how to plug it in wxmaxima is it possible if you can show me
thanks very much 
Define a function f(x) (to find arclength)
f(x):=......
Find its derivative:
diff(f(x),x)
Copy and paste the result and assign it to another function, say f1(x):
f1(x):=....paste....
Go to the Calculus/integrate function.
For the integrand, input:
sqrt(1+f1(x)^2)
Input the limits of integration.
check the 'numerical integration' box.
leave the method as default, Romberg or the other one will both work. Best is try both and compare. This will give you an idea of the accuracy.
Click OK and wait.
Post if you could use further help. 
okay so for the first f(x) i plug in cos(x^2 +(100493/100000))find the derivative then do i do the same for y=y=1+xX^2 ?

Exactly! Repeat all the steps for the polynomial.
Since the two functions are to be integrated within the same interval, you are better off doing them separately. 
okay so i put y=1+xX^2 found the derivative 12*x then i pluged that in into sqrt(1+12*x)^2) then i did the romberg thing so is this right i got 1.4336 for this one

WEll THANKSSSS ALOTTTTTTTTTTTTTTTTT!

Did your length for the cos function match mine at about 3.4?
Glad that everything worked out!
À la prochaine! 
Oops, I don't think 1.4 is right for the polynomial.
Did you use sqrt(1+(dy/dx)^2)?
Your expression sqrt(1+12*x)^2) has a missing parenthesis.
I got 2.29 for the polynomial, and 3.4 for the cos function.
Respond to this Question
Similar Questions

calculus wxmaxima
does anyone know how to approximate the are and circumfrence of the region bounded by the given curves y=cos(x^2 +(100493/100000)), y=1+xX^2 i already did the area but i need help with the circumference 
CALCULUS WXMAXIMA HELP PLEASE!
y=log(100493/40000x), y=atan(100493/40000x), y=exp(100493/40000x) approximate the region bounded by the given curves. be sure to specify a range of x and y that results in a good picture of the region. you need two integral to represent … 
wxmaxima help math mate!
one expression is y=log(100493/40000)x the x is next to the (100493/40000) same with the other expression y=atan(100493/40000)x, y=exp(100493/40000x) approximate the region bounded by the given curves. be sure to specify a range … 
calculus
find the centroid of the plane region bounded by the curves y = cos x, y=sinx, x=0, 
CALCULUS WXMAXIMA !!PLEASE!
y=log(100493/40000*x1) y=atan(100493/40000*x+1) y=exp(100493/40000*x+1) Note you will need 2 integrals to represent the area. Approximate the area of the region bounded by the given curves. I can do it with two but kinda struggling … 
Calculus [rotation of region bounded by curves]
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y=3x^2, x=1, y=0 about the xaxis 
mathcalculus 2
Consider the given curves to do the following. 64 y = x^3, y = 0, x = 4 Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about y = 1. 
math, calculus
1. Consider the region bounded by the curves y=x^2+x12, x=5, and x=5 and the xaxis. A. Set up a sum of integrals, not containing an absolute value symbol, that can be used to find the area of this region. B. Find the area of the … 
Calculus
find the area of the region bounded by the curves y=x^21 and y =cos(x) 
calculus 2
Use a graph to find approximate xcoordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. (Round your answer to two decimal places.) y = 8x^2− 3x, …