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Practice: Area inside Polar Curves
Related Topics
Wize University Calculus 2 Textbook > Parametric & Polar Curves
Calculus w/ Polar Coordinates
8 Activities
Practice Question
Write the integral representing the area of the inner loop of
r
=
2
+
4
sin
θ
.
r = 2 + 4 \sin \theta.
r
=
2
+
4
sin
θ
.
A
=
1
2
∫
π
/
6
5
π
/
6
(
4
sin
θ
)
2
d
θ
A=\frac{1}{2}{\displaystyle\int}^{5\pi/6}_{\pi/6}(4\sin\theta)^2\de{\theta}
A
=
2
1
∫
π
/6
5
π
/6
(
4
sin
θ
)
2
d
θ
A
=
2
∫
π
/
6
5
π
/
6
(
4
sin
θ
)
2
d
θ
A=2{\displaystyle\int}^{5\pi/6}_{\pi/6}(4\sin\theta)^2\de{\theta}
A
=
2
∫
π
/6
5
π
/6
(
4
sin
θ
)
2
d
θ
A
=
1
2
∫
π
/
6
5
π
/
6
(
2
+
4
sin
θ
)
2
d
θ
A=\frac{1}{2}{\displaystyle\int}^{5\pi/6}_{\pi/6}(2+4\sin\theta)^2\de{\theta}
A
=
2
1
∫
π
/6
5
π
/6
(
2
+
4
sin
θ
)
2
d
θ
A
=
1
2
∫
7
π
/
6
11
π
/
6
(
2
+
4
sin
θ
)
2
d
θ
A=\frac{1}{2}{\displaystyle\int}^{11\pi/6}_{7\pi/6}(2+4\sin\theta)^2\de{\theta}
A
=
2
1
∫
7
π
/6
11
π
/6
(
2
+
4
sin
θ
)
2
d
θ
A
=
2
∫
7
π
/
6
11
π
/
6
(
2
+
4
sin
θ
)
2
d
θ
A=2{\displaystyle\int}^{11\pi/6}_{7\pi/6}(2+4\sin\theta)^2\de{\theta}
A
=
2
∫
7
π
/6
11
π
/6
(
2
+
4
sin
θ
)
2
d
θ
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Check Submission
More Calculus w/ Polar Coordinates Questions:
Practice: Polar Curve Tangent
Find the slope of the tangent line to the curve
r
=
sec
2
θ
csc
θ
r = \sec^2 \theta \csc\theta
r
=
sec
2
θ
csc
θ
at
θ
=
π
/
6.
\theta = \pi/6.
θ
=
π
/6.
Practice: Area inside Polar Curves
Practice Question
Write the integral representing the area of the inner loop of
r
=
2
+
4
sin
θ
.
r = 2 + 4 \sin \theta.
r
=
2
+
4
sin
θ
.
Practice: Polar Curve Tangent
Practice Question
Find the slope of the tangent line to the curve
r
=
sec
2
θ
csc
θ
r = \sec^2 \theta \csc\theta
r
=
sec
2
θ
csc
θ
at
θ
=
π
/
6.
\theta = \pi/6.
θ
=
π
/6.
Practice: Polar Curve Tangent
Practice Question
Find the slope of the tangent line to the curve
r
=
sec
2
θ
csc
θ
r = \sec^2 \theta \csc\theta
r
=
sec
2
θ
csc
θ
at
θ
=
π
/
6.
\theta = \pi/6.
θ
=
π
/6.
Practice: Area inside Polar Curves
Practice Question
Write the integral representing the area of the inner loop of
r
=
2
+
4
sin
θ
.
r = 2 + 4 \sin \theta.
r
=
2
+
4
sin
θ
.
Practice: Area inside Polar Curves
Practice Question
Write the integral representing the area of the inner loop of
r
=
2
+
4
sin
θ
.
r = 2 + 4 \sin \theta.
r
=
2
+
4
sin
θ
.
Practice: Polar Curve Tangent
Practice Question
Find the slope of the tangent line to the curve
r
=
sec
2
θ
csc
θ
r = \sec^2 \theta \csc\theta
r
=
sec
2
θ
csc
θ
at
θ
=
π
/
6.
\theta = \pi/6.
θ
=
π
/6.