Final answer:
To find the exact length of the curve y = x - x² sin⁻¹x, use the formula for arc length and integrate the expression with respect to x.
Step-by-step explanation:
To find the exact length of the curve y = x - x² sin⁻¹x, we can use the formula for arc length: L = ∫sqrt(1 + (dy/dx)²) dx. In this case, dy/dx is equal to 1 - 2x sin⁻¹x. We need to integrate this expression with respect to x from the lower limit to the upper limit of x. Once we find the indefinite integral, we can evaluate it and find the length of the curve.