Final answer:
To find the arc length of the graph of the function x = 13(y² - 2)^(3/2) over the interval 0 ≤ y ≤ 2, we can use the formula for arc length and follow the steps to solve it.
Step-by-step explanation:
Arc length is the distance along a curved line, and it is a measure of the actual length of a part of a curve. The formula for calculating the arc length depends on whether you're dealing with a portion of a circle or a more general curve.
To find the arc length of the graph of the function x = 13(y² - 2)^(3/2) over the interval 0 ≤ y ≤ 2, we can use the formula for arc length:
Arc Length = ∫√(1 + (dy/dx)²) dx
First, we need to find dy/dx by taking the derivative of x with respect to y. After finding dy/dx, we substitute it into the arc length formula. Finally, we integrate the resulting expression over the given interval to find the arc length.