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We can calculate this using arc length formula.
![L= \int\limits^a_b { \sqrt[]{1+ (\frac{dy}{dx} } )^2} \, dx](https://tex.z-dn.net/?f=L%3D%20%5Cint%5Climits%5Ea_b%20%7B%20%5Csqrt%5B%5D%7B1%2B%20%28%5Cfrac%7Bdy%7D%7Bdx%7D%20%7D%20%29%5E2%7D%20%5C%2C%20dx%20)
The first step is to find the derivative of the given function.
Now we plug this back into original integral.
![L= \int\limits^a_b { \sqrt[]{1+ 9x} \, dx](https://tex.z-dn.net/?f=L%3D%20%5Cint%5Climits%5Ea_b%20%7B%20%5Csqrt%5B%5D%7B1%2B%209x%7D%20%5C%2C%20dx%20)
We solve this integral using substituition u=9x+1. This way we end up solving elementary integral.
A final solution is:
Finaly we get that arc lenght is:
The first step is to find the derivative of the given function.
Now we plug this back into original integral.
We solve this integral using substituition u=9x+1. This way we end up solving elementary integral.
A final solution is:
Finaly we get that arc lenght is:
Answer:
f[g(1)]=6.
Explanation:
Given f(n) and g(n) defined below:
First, we evaluate g(1):
Therefore:
Therefore, f[g(1)]=6.