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# Finding the length of an arc (Calculus)?

To go about finding this arc length how would I do it:

"the function is x^3/2 with an interval of x = 4 to x = 9"

### 1 Answer

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- BryceLv 72 months ago
L= ∫[4 to 9] √[1 + ((3/2)x^0.5)²] dx

= ∫[4 to 9] √[1 + (9/4)x] dx

= (2/3)(4/9)(1 + (9/4)x)^3/2

= (8/27)[(85/4)^3/2 - 10^3/2]

≈ 19.655

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