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+x-X^2
i already did the area but i need help with the circumference
Do follow-up with the same post whenever possible.
The answer has been posted:
http://www.jiskha.com/display.cgi?id=1297900781
i found it but like i understand what youre saying i just don't know how to plug it in wxmaxima is it possible if you can show me
thanks very much
To approximate the circumference of the region bounded by the given curves, you can use numerical integration to find the length of the curves.
The curve y = cos(x^2 + (100493/100000)) and y = 1 + x - X^2 intersect at certain points. To find these points, set the two equations equal to each other:
cos(x^2 + (100493/100000)) = 1 + x - X^2
This equation cannot be solved analytically, so we will need to use numerical methods to approximate the solutions.
One approach is to use the graphical method. Plot the two curves on a graphing calculator or a graphing software and find the approximate x-values where they intersect.
Another approach is to use a numerical solver such as Newton's method or the bisection method. These methods allow you to find the roots of an equation (i.e., the x-values at which the equation equals zero). By solving the equation cos(x^2 + (100493/100000)) - (1 + x - X^2) = 0, you can find the x-values where the curves intersect.
Once you have the x-values of the intersection points, you can use numerical integration to approximate the circumference. Divide the region bounded by the curves into small sections and approximate the length of each section. Then, sum up the lengths of all the sections to obtain an approximation of the total circumference.
You can use various methods for numerical integration, such as the Trapezoidal Rule or Simpson's Rule. These methods work by approximating the curve as a series of straight line segments or curves, and then calculating the lengths of these segments or curves.
By following these steps, you should be able to approximate the circumference of the region bounded by the given curves.