Arc length of curves
Applications of integration · Mathematics
Study notes
Q: Find the length of y = (2/3)x^(3/2) from x = 0 to x = 3. dy/dx = x^(1/2). So 1 + (dy/dx)^2 = 1 + x. L = integral 0 to 3 of sqrt(1+x) dx. Let u = 1+x: integral 1 to 4 of sqrt(u) du = [2u^(3/2)/3] 1 to 4 = (2/3)(8 - 1) = 14/3.