# find a formula for arc length of y=3t-2 from t=0 to t=x

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### 1 Answer

The formula for the arc length of y = 3t - 2 from t = 0 to t = x has to be determined.

The arc length of a curve represented by y = f(x) from x = a to x = b is given by the integral:

`int_a^b sqrt(1+ (dy/dx)^2) dx`

For y = 3t - 2, `dy/(dt) = 3`

`int_0^x sqrt(1+ (dy/(dt))^2) dt`

= `int_0^x sqrt(1+ 9) dt`

= `int_0^x sqrt 10 dt`

= `sqrt 10*(x - 0)`

= `sqrt 10*x`

**The formula for the arc length of y = 3t - 2 from t = 0 to t = x is **`sqrt 10*x`