AP Calculus BC Quiz
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PARAMETRIC, POLAR, AND VECTOR FUNCTIONS
Question 1
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Which integral gives the area enclosed by
r
=
1
+
cos
θ
r=1+\cos\theta
r
=
1
+
cos
θ
and
r
=
1
−
cos
θ
r=1-\cos\theta
r
=
1
−
cos
θ
?
A
1
2
∫
0
2
π
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
\dfrac12\displaystyle\int_{0}^{2\pi}\big[(1+\cos\theta)^2-(1-\cos\theta)^2\big]d\theta
2
1
∫
0
2
π
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
B
1
2
∫
−
π
/
2
π
/
2
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
\dfrac12\displaystyle\int_{-\pi/2}^{\pi/2}\big[(1+\cos\theta)^2-(1-\cos\theta)^2\big]d\theta
2
1
∫
−
π
/2
π
/2
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
C
1
2
∫
0
π
[
(
1
−
cos
θ
)
2
−
(
1
+
cos
θ
)
2
]
d
θ
\dfrac12\displaystyle\int_{0}^{\pi}\big[(1-\cos\theta)^2-(1+\cos\theta)^2\big]d\theta
2
1
∫
0
π
[
(
1
−
cos
θ
)
2
−
(
1
+
cos
θ
)
2
]
d
θ
D
1
2
∫
0
π
/
2
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
\dfrac12\displaystyle\int_{0}^{\pi/2}\big[(1+\cos\theta)^2-(1-\cos\theta)^2\big]d\theta
2
1
∫
0
π
/2
[
(
1
+
cos
θ
)
2
−
(
1
−
cos
θ
)
2
]
d
θ
E
∫
−
π
/
2
π
/
2
[
(
1
+
cos
θ
)
−
(
1
−
cos
θ
)
]
d
θ
\displaystyle\int_{-\pi/2}^{\pi/2}\big[(1+\cos\theta)-(1-\cos\theta)\big]d\theta
∫
−
π
/2
π
/2
[
(
1
+
cos
θ
)
−
(
1
−
cos
θ
)
]
d
θ
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