Question

Set up an integral to find the length of the curve defined by y = 5x^(3/2) + 5 from x = 3 to x = 8, then evaluate it.

L = ∫[3 to 8] dx = ________

Answer 1

To find the length of the curve defined by the equation y = 5x^(3/2) + 5 from x = 3 to x = 8, we can use the formula for arc length of a curve and integrate the expression.

Step-by-step explanation:

To find the length of the curve defined by the equation y = 5x^(3/2) + 5 from x = 3 to x = 8, we can use the formula for arc length of a curve: L = ∫(sqrt(1 + (dy/dx)^2) dx, where dy/dx represents the derivative of y with respect to x.

In this case, dy/dx = (15/2)x^(1/2).

Substituting this into the formula, we have L = ∫(sqrt(1 + (15/2)^2x dx) from 3 to 8.

Integrating this expression will give us the length of the curve from x = 3 to x = 8.