A curve C is defined by the parametric equations x(t)=f(t) and y(t)=t, where f is a differentiable function. Which of the following gives the length of curve C from t=−1 to t=8 ? All answers are integrated from -1 to 8

A= √(f(t)+t dt)
B= √(((f(t))^2)+t^2 dt)
C= √(f'(t)+1 dt)
D= √(((f'(t))^2)+1 dt)

the correct answer is 1: 2

step-by-step explanation:

hope this your welcome : )

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

this cant be answered without the graph. you may need to add it.