Main content

AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 9

Lesson 8: Finding the area of the region bounded by two polar curves

Area between two polar curves

Let R be the region in the first and second quadrants that is inside the polar curve r, equals, 3 and inside the polar curve r, equals, 2, plus, 2, cosine, left parenthesis, theta, right parenthesis, as shown in the graph. The curves intersect at theta, equals, start fraction, pi, divided by, 3, end fraction.

Which integral represents the area of R?

(Choice A)
start fraction, 1, divided by, 2, end fraction, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 3, end fraction, end superscript, 9, d, theta, plus, start fraction, 1, divided by, 2, end fraction, integral, start subscript, start fraction, pi, divided by, 3, end fraction, end subscript, start superscript, pi, end superscript, left parenthesis, 2, plus, 2, cosine, left parenthesis, theta, right parenthesis, right parenthesis, squared, d, theta
(Choice B)
start fraction, 1, divided by, 2, end fraction, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 3, end fraction, end superscript, left parenthesis, 9, minus, left parenthesis, 2, plus, 2, cosine, left parenthesis, theta, right parenthesis, right parenthesis, squared, right parenthesis, d, theta
(Choice C)
start fraction, 1, divided by, 2, end fraction, integral, start subscript, 0, end subscript, start superscript, pi, end superscript, left parenthesis, 9, minus, left parenthesis, 2, plus, 2, cosine, left parenthesis, theta, right parenthesis, right parenthesis, squared, right parenthesis, d, theta
(Choice D)
start fraction, 1, divided by, 2, end fraction, integral, start subscript, 0, end subscript, start superscript, start fraction, pi, divided by, 6, end fraction, end superscript, 9, d, theta, plus, start fraction, 1, divided by, 2, end fraction, integral, start subscript, start fraction, pi, divided by, 6, end fraction, end subscript, start superscript, start fraction, pi, divided by, 3, end fraction, end superscript, left parenthesis, 2, plus, 2, cosine, left parenthesis, theta, right parenthesis, right parenthesis, squared, d, theta

Stuck?

AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 9

Problem