The total cost of a new calculator is $81.05. This price includes a 10% discount followed by a 6.5% sales tax. What was the orig
1 answer:
You might be interested in
Answer:
The integral for the arc of length is:
By using Simpon’s rule we get: 1.5355453
And using technology we get: 2.3020
The approximation is about 33% smaller than the exact result.
Explanation:
The formula for the length of arc of the function f(x) in the interval [a,b] is:
We need the derivative of the function:
And we need it squared:
Then the integral is:
Now, the Simposn’s rule with n=4 is:
In this problem:
So, the Simposn’s rule formula becomes:
Then simplifying a bit:
Then we just do those computations and we finally get the approximation via Simposn's rule:
While when we do the integral by using technology we get: 2.3020.
The approximation with Simpon’s rule is close but about 33% smaller: