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Find the arc length of the curve y = x^³/² from x = 0 to x=4.

User Nobel
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Final answer:

To find the arc length of the curve y = x^³/² from x = 0 to x=4, you can use the formula As = ∫(sqrt(1 + (dy/dx)²)) dx and apply it to the given curve.

Step-by-step explanation:

The arc length of a curve can be found using the formula:

As = ∫(sqrt(1 + (dy/dx)²)) dx

Applying this formula to the given curve y = x^(3/2) from x = 0 to x = 4, we have:

As = ∫(sqrt(1 + (3/2)x^(1/2)²)) dx

Integrating this expression will give us the arc length of the curve.

User Ahmad Sattout
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