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Integral Calculus

Course: Integral Calculus > Unit 4

Lesson 5: Arc length: polar curves

Arc length of polar curves

Which of the following integrals gives the arc length of the part of the three-petal flower space, r, equals, 2, cosine, left parenthesis, 3, theta, right parenthesis, space pictured above that lies in space, start color #df0030, start text, Q, u, a, d, r, a, n, t, space, I, end text, end color #df0030?

(Choice A)
space, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 6, end fraction, end superscript, square root of, 4, cosine, squared, left parenthesis, 3, theta, right parenthesis, plus, 36, sine, squared, left parenthesis, 3, theta, right parenthesis, end square root, d, theta
(Choice B)
space, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 2, end fraction, end superscript, 2, cosine, squared, left parenthesis, 3, theta, right parenthesis, d, theta
(Choice C)
space, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 2, end fraction, end superscript, square root of, 4, cosine, squared, left parenthesis, 3, theta, right parenthesis, plus, 36, sine, squared, left parenthesis, 3, theta, right parenthesis, end square root, d, theta
(Choice D)
space, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 6, end fraction, end superscript, 2, d, theta
(Choice E)
space, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 2, end fraction, end superscript, 2, d, theta

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Integral Calculus

Course: Integral Calculus > Unit 4

Problem