Question

Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curve on the given interval y=2cos 3x on -- An integral that gives the arc length is a d x (Type exact answers.) Enter your answer in each of the answer boxes.

Answer 1

The arc length of
`y=2\cos(3x)` on the interval
`[a,b]` is

`\displaystyle \int_a^b √(1 + (y')^2) \, dx = \int_a^b √(1 + (-6\sin(3x))^2) \,dx = \boxed{\int_a^b √(1+36\sin^2(3x)) \, dx}`