Answer: Find the angle between the diagonal of a cube and the diagonal of one of its

Chapter 10, Problem 74

(choose chapter or problem)

Which integral yields the arc length of \(r=3(1-\cos 2 \theta)\)? State why the other integrals are incorrect.

(a) \(3 \int_{0}^{2 \pi} \sqrt{(1-\cos 2 \theta)^{2}+4 \sin ^{2} 2 \theta} d \theta\)

(b) \(12 \int_{0}^{\pi / 4} \sqrt{(1-\cos 2 \theta)^{2}+4 \sin ^{2} 2 \theta} d \theta\)

(c) \(3 \int_{0}^{\pi} \sqrt{(1-\cos 2 \theta)^{2}+4 \sin ^{2} 2 \theta} d \theta\)

(d) \(6 \int_{0}^{\pi / 2} \sqrt{(1-\cos 2 \theta)^{2}+4 \sin ^{2} 2 \theta} d \theta\)

Text Transcription:

r=3(1-cos 2 theta)

3 int_0^2 pi sqrt (1-cos 2 theta)^2+4 sin^2 2 theta d theta

12 int_0^pi/4 sqrt (1-cos 2 theta)^2+4 sin^2 2 theta d theta

3 int_0^pi sqrt (1-cos 2 theta)^2+4 sin^2 2 theta d theta

6 int_0^pi/2 sqrt (1-cos 2 theta)^2+4 sin^2 2 theta d theta