Find the length of the curve. r(t) = 2 i + t2 j + t3 k, 0 ≤ t ≤ 1

Length of a curve is the length of its plot its curve. The length of the given curve for given range of t is: L = 1.44 units approx.

If the curve has position vector p(x) for value of x ranging from x = a to x = b,

then, the curve's length is calculated as:

units.

For the given case, we have:

Position vector =  

Its differentiation gives:

Its non negative magnitude is: ||R'(t)|| =

Thus, as t ranges from a = 0 to b = 1, thus, length of the curve is:

Thus,

The length of the given curve for given range of t is: L = 1.44 units approx.

Learn more about length of the curve here:

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curve equation is

 ,0≤ t≤ 1

now taking the differentiation

now taking the modulus

                                      =

now taking the integration

length of the curve =  

now put the value v=  4 + 9t²

                              dv= 18 tdt

now put this value in the above equation

we get

length of the curve =

now taking integation we get and put the value of the v

we get

= × ×

=

now find out the length of the curve in the interval from 0 to 1.

length of the curve

Hence proved

the answer is (-8,-5)

step-by-step explanation:

the endpoint to midpoint is half the length. the length is (-2,-1) so when you are at the midpoint just add it to it to find your answer -6+(-2)= -8 and -4+(-1)=-5 so (-8,-5)

the answer is 11.2 (i know i’m late)