3–6. Setting up arc length integrals Write and simplify, but d...

Question

3–6. Setting up arc length integrals Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curves on the given interval.

y = 2 cos 3x on [−π,π]

Accepted Answer

Welcome back everyone. Write and simplify, but do not evaluate an integral with respect to x that gives the length of the curve Y equals 5 cosine for X on the interval from negative pi divided by 2 up to pi divided by 2. For this problem, let's write down the arkland formula. Let's recall that L equals the integral from A to B of square root of 1 plus the derivative of Y with respect to X squared X. What we want to do is simply evaluate A, B, and the derivative D Y divided by the X to get our formula. Let's begin with the limits of integration. A corresponds to the lower value of the interval, and that would be negative. I divided by 2. B, which is the upper limit of integration, would be the upper end point, and that would be pi divided by 2. Our next step is to. Find the derivatived Y divided by d X, which is the derivative of 5 cosine 4 x. What we can do is simply factor out 5. We can find the derivative of cosine, which is negative sign, right? So we get negative sign of 4 X. And according to the chain rule, we're multiplying by the derivative of 4 X. This is equal to. Now we get a negative sign. We then take 5 multiplied by 4 because the derivative of X is 1, so that's -20. Sign of 4 X. Well then, so now we have our derivative. We can find the square of this derivative. We're going to square -20. Sign for X. Now -202 is 400. Sign for X squad that's going to be squared for X, and we can basically substitute. This expression into our formula. So the R L is going to be the integral from negative pi divided by 2 up to pi divided by 2 of square root of 1 + 400 squared 4 XDX. And that will be our final answer for this problem. Thank you for watching.

3–6. Setting up arc length integrals Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curves on the given interval.y = 2 cos 3x on [−π,π]

Watch next

3–6. Setting up arc length integrals Write and simplify, but do not evaluate, an integral with respect to x that gives the length of the following curves on the given interval.
y = 2 cos 3x on [−π,π]