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Find the arc length of y = 2x² on the interval 0 ≤ x ≤ 2.

User Arva
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Final answer:

To find the arc length of the equation y = 2x² on the interval 0 ≤ x ≤ 2, we can use the formula for arc length.

Step-by-step explanation:

To find the arc length of the equation y = 2x² on the interval 0 ≤ x ≤ 2, we need to use the formula for arc length.

The formula for arc length in terms of a function y = f(x) is given by L = ∫√(1 + (f'(x))²) dx, where f'(x) represents the derivative of f(x).

For y = 2x², we need to find f'(x) = 4x. Substituting this into the formula, we get L = ∫√(1 + (4x)²) dx.

Integrating this expression from x = 0 to x = 2 will give us the arc length.

User Dobrivoje
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