Careful; (dy/dx)^2 = x^2 cos^2(x) + 2x sin x cos x + sin^2(x).
<span>So, the arc length equals </span>
<span>∫(x = 0 to 2π) √[1 + (x^2 cos^2(x) + 2x sin x cos x + sin^2(x))] dx </span>
<span>= ∫(x = 0 to 2π) √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)] dx, via double angle identity. </span>
<span>Let Δx = (2π - 0)/10 = π/5. </span>
<span>Using Simpson's Rule with n = 10, this integral approximately equals </span>
<span>((π/5)/3) * [f(0) + 4 f(π/5) + 2 f(2π/5) + 4 f(3π/5) + 2 f(4π/5) + 4 f(π) + 2 f(6π/5) + 4 f(7π/5) + 2 f(8π/5) + 4 f(9π/5) + f(2π)], </span>
<span>where f(x) = √[1 + x^2 cos^2(x) + x sin(2x) + sin^2(x)]. </span>
<span>------- </span>
<span>I hope this helps!</span>
Answer:
angle SXV
Step-by-step explanation:
13 i think idk i’m pretty sure it’s 13 ya i think it is
Answer:
R = 6S/T
Step-by-step explanation:
R ∝ S/ T
》R = kS/ T
》k = RT/ S
If R = 8 when S = 4 and T = 3
then, k = (8 × 3)/ 4
k = 6
∴ R = (6 × S)/ T
