Step-by-step explanation:
Given
The function is 
for
, we will check the values of
and 
Take 3 and 4

Similarly,

Thus, 
Also,
is 1 i.e. a constant value. So, the function is increasing linearly for the given interval.
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:
A because the intersection point of the graph is 3x-8y=19
Step-by-step explanation:
the eqn is 3x-2y+10=0
slope m=-3/-2=3/2 (m=(-xcoeff/ycoeff)
eqn is
y-y1=m(x-x1)
y+5=3/2(x-2)
2y+10=3x-6
3x-2y-16=0