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AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 9

Lesson 7: Finding the area of a polar region or the area bounded by a single polar curve

Area bounded by polar curves

AP.CALC: CHA‑5 (EU), CHA‑5.D (LO), CHA‑5.D.1 (EK), CHA‑5.D.2 (EK)

Let R be the region in the first and second quadrants enclosed by the polar curve r, left parenthesis, theta, right parenthesis, equals, sine, squared, left parenthesis, theta, right parenthesis, as shown in the graph.

Which integral represents the area of R?

(Choice A)
integral, start subscript, 0, end subscript, start superscript, 2, pi, end superscript, start fraction, 1, divided by, 2, end fraction, sine, start superscript, 4, end superscript, left parenthesis, theta, right parenthesis, d, theta
(Choice B)
integral, start subscript, 0, end subscript, start superscript, 2, pi, end superscript, start fraction, 1, divided by, 2, end fraction, sine, squared, left parenthesis, theta, right parenthesis, d, theta
(Choice C)
integral, start subscript, 0, end subscript, start superscript, pi, end superscript, start fraction, 1, divided by, 2, end fraction, sine, squared, left parenthesis, theta, right parenthesis, d, theta
(Choice D)
integral, start subscript, 0, end subscript, start superscript, pi, end superscript, start fraction, 1, divided by, 2, end fraction, sine, start superscript, 4, end superscript, left parenthesis, theta, right parenthesis, d, theta

Stuck?

AP®︎/College Calculus BC

Course: AP®︎/College Calculus BC > Unit 9

Problem