Question

Write and simplify the integral that gives the arc length of the following curve on the given interval b. If necessary, use technology to evaluate or approximate the integral. y:31n x, for 2sxs5 a. The integral that gives the arc length of the curve is L dx &The arc length of the curve is approximately (Round to three decimal places as needed.)

Answer 1

Answer:

L = 4.103

Step-by-step explanation:

we have length of curve

$L = \int\limits^b_a {\sqrt{(f'(x))²+1} } \, dx$

where $f(x) = d/dx(3*in(x)) = 3/x$

substituting for f(x), we have $L = \int\limits^5_2 {\sqrt{(3/x)²+1} } \, dx$

(since the limit is 2≤ x ≤5)

solving,  $L = \int\limits^5_2 {\sqrt{9/x²+1} } \, dx$

Simplifying this integral, we have

L = 4.10321