Question

a) Set up the area integrals of the region that lies outside the circle $r = 5$ and inside the cardioid $r = 5(1 + \sin \theta)$.\\ To denote $\theta$ use variable $t$.\\ Thus you have to evaluate (without using symmetry)\\ where $a = \boxed{\qquad}$, $b = \boxed{\qquad}$, and $f(\theta) = \boxed{\qquad}$ \\ $\text{Area} = \int_a^b f(\theta) d\theta$\\ b) Now, set up the area integrals of the region that lies inside the circle $r = 5$ and outside the cardioid $r = 5(1 + \sin \theta)$.\\ To denote $\theta$ use variable $t$.\\ Thus you have to evaluate (without using symmetry)\\ where $c = \boxed{\qquad}$, $d = \boxed{\qquad}$, and $g(\theta) = \boxed{\qquad}$ \\ $\text{Area} = \int_c^d g(\theta) d\theta$

          a) Set up the area integrals of the region that lies outside the circle $r = 5$ and inside the cardioid $r = 5(1 + \sin \theta)$.\\
To denote $\theta$ use variable $t$.\\
Thus you have to evaluate (without using symmetry)\\
where $a = \boxed{\qquad}$, $b = \boxed{\qquad}$, and $f(\theta) = \boxed{\qquad}$ \\
$\text{Area} = \int_a^b f(\theta) d\theta$\\
b) Now, set up the area integrals of the region that lies inside the circle $r = 5$ and outside the cardioid $r = 5(1 + \sin \theta)$.\\
To denote $\theta$ use variable $t$.\\
Thus you have to evaluate (without using symmetry)\\
where $c = \boxed{\qquad}$, $d = \boxed{\qquad}$, and $g(\theta) = \boxed{\qquad}$ \\
$\text{Area} = \int_c^d g(\theta) d\theta$

a) Set up the area integrals of the region that lies outside the circle r = 5 and inside the cardioid r = 5(1 + sinθ).

To denote θ use variable t.

Thus you have to evaluate (without using symmetry)

where a =, b =, and f(θ) =

Area = ^b f(θ) dθ

b) Now, set up the area integrals of the region that lies inside the circle r = 5 and outside the cardioid r = 5(1 + sinθ).

To denote θ use variable t.

Thus you have to evaluate (without using symmetry)

where c =, d =, and g(θ) =

Area = ^d g(θ) dθ

Added by Victoria B.

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