first property is that your function is even meaning that
second (as seen on the image to) means that is above x-axis
third just say that surface under it is 1
does this helps you in any way ? what kind of functions can be even ?
Hint: for the first .... will give you that and second ?
The images are only examples of some functions that have the given properties. That does not mean that every function that satisfies those properties will be even. And a non-even function might not be odd.
Here is a non-even function that probably satisfies the given properties, please check to be sure :
Hello, CHARLIEDANCE!
Assuming that the first graph is a down-opening parabola,
. . symmetric to the -axis, we have: .
The -intercepts are
. . So we have: .
The function (so far) is: .
The area on is 1:
. .
. . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
Therefore: .
Assuming that the second graph is a down-opening quartic,
. . symmetric to the -axis, we have: .
The -intercepts are
. . So we have: .
The function (so far) is: .
The area on is 1:
. .
. . . . . . .
. . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
Therefore: .
I'll let you show that the arc lengths are different . . .
Hey Guys thanks you for the help. thank you yeKciM and sorobaN for giving step by step it helped me really under stood it!
Soroban i have drawn the graphs on excel and they look good to me.
I have tried to show that the arc lengths are different to 4 decimal places by using :
By one of my other class mates said that i could also use the Trapezoidal rule of the Simpson's Rule and that i should try to get the smallest possible integral.
Is this true ? How would i go about that using the above formula? Be cause with what i have im not sure if i i can go even further or have the need to use the Simpson's Rule or Trapezoidal Rule.