Question

a. Write and simplify the integral that gives the arc length of the following curve on the given integral. b If necessary, use technology to evaluate or approximate the integral. y = sin(2x) on [0, pi/2] Set up the integral that gives the arc length of the curve. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers.) A. L = integral -1 to 1() dy B. L = integral 0 to pi/2 ()dx

Answer 1

Answer:

\int\limits^{\pi/2} _0 (1+4cos^{2} (2x)dx

Step-by-step explanation:

Arc length is calculated by dividing the arcs in to small segments ds

By pythagoren theorem

$ds^2=dx^2+dy^2$

then integrate ds to get arc length.

We are given a function as

y = sin 2x in the interval  [0, pi/2]

To find arc length in the interval

Arc length $s =\int\limits^{\pi/2} _0 {1+y'^2} \, dx \\=\int\limits^{\pi/2} _0 (1+4cos^{2} (2x) )dx$

Hence arc length would be

B) $\int\limits^{\pi/2} _0 (1+4cos^{2} (2x)dx$