find a curve that passes through the point (1,-2 ) and has an arc length on the interval 2 6 given by 1 144 x^-6

or

Step-by-step explanation:

Given

--- Point

The arc length of a function on interval [a,b]:  

By comparison:

Take square root of both sides

Split:

or

To solve fo f(x), we make use of:

For:

Integrate:

We understand that it passes through .

So, we have:

Make c the subject

becomes

For:

Integrate:

We understand that it passes through .

So, we have:

Make c the subject

becomes

54.864 meters

step-by-step explanation: