What is the arc length of the curve segment y = x^4 from (0,0) to (1,1)?

Question

Could it possibly be one of the following ....

1.600
1.548
1.479
1.641
1.673

Answer 1

Use the formula for arc length of f(x) as x travels from x_1 to x_2:

Arc Length = integral from x_1 to x_2 of sqrt(1 + f'(x)^2).

In this case:

Integral from 0 to 1 of sqrt(1 + (4x^3)^2).

= about 1.600.