calculus homework help

Question

Find the length of the graph of (y+2)² = (x-3)³ from the point (4, -1) to the point (7, 6). Check the integral calculation using at TI-83 or TI-84 calculator.

Answer 1

Solve for y first

y = ±(x-3)^3/2+2

The curve is split between upper and lower components. Since the problem's limits are (4, -1) to (7,6), we

are only interested in the upper curve.

dy/dx = (3/2)(x-3)^1/2

(dy/dx)²=(9/4)(x-3)

Length=∫₄⁷ √(1+9(x-3)/4) dx = (1/2)∫₄⁷ √(9x-23)dx

If you let u = 9x-23, can you finish the integration?