Question

Set up, but do not evaluate, an integral for the length of the curve.
x=y+y⁵, 1 ≤ y ≤ 6

Answer 1

To set up the integral for the length of the curve x = y + y^5, use the arc length formula and solve for x in terms of y.

Step-by-step explanation:

To set up the integral for the length of the curve, you can use the arc length formula. The arc length formula for a curve y = f(x) is given by:

L = ∫ab √(1+(f'(x))²) dx

In this case, the curve is given by x = y + y^5 and the limits of integration are 1 ≤ y ≤ 6. We need to solve for x in terms of y and find the derivative of x with respect to y before setting up the integral.