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Determine lenght of the arc of the function f(x)=2x³/₂ from x=2 to x=5.

User Ovangle
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Final answer:

The length of the arc of the function f(x) = 2x³/₂ from x = 2 to x = 5 is 27 units.

Step-by-step explanation:

To find the length of the arc of the function f(x) = 2x³/₂ from x = 2 to x = 5, we need to integrate the function over the given interval.

∫[2,5] 2x³/₂ dx

Using the power rule of integration, we can rewrite the function as:

= ∫[2,5] 2x² dx

= [x³/₂] from 2 to 5

= (5³/₂) - (2³/₂)

= 31 - 4

= 27 units.

User Jammy Lee
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