A student will use a numeric integration feature that accepts an integrand on the…

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A student will use a numeric integration feature that accepts an integrand

g(\theta)

on the interval

[a,b]

and then plans to multiply the result by

\tfrac12

to approximate the area enclosed by the polar curve

r=f(\theta)

for

a\le\theta\le b

. Which choice for

g(\theta)

will produce the correct area estimate? (a)

\tfrac12\,f(\theta)^{2}

(b)

f(\theta)

(c)

f(\theta)^{2}

(d)

f(\theta)^{2}\sin\theta