Question

find the area of the region that lies inside the first curve and outside the second curve. r = 7 cos(theta), r = 3 + cos(theta)

Answer 1

Answer:

23.5

Given:

r = 7 cos(θ ),

r = 3 + cos(θ )

Step-by-step explanation:

Here the red colored graph is r=7cosθ and the blue colored graph is

r=3+cosθ

From the above figure we can see that

θ  varies from θ $=-\frac{\pi }{3} to$ θ =$\frac{\pi }{3}$

r varies from r=3+cosθ  to r=7cosθ

The total area of the yellow shaded region is twice the area of the yellow region above x axis thus, total area is calculated as follows

A$=2\int\limits^\frac{\pi }{3} _0$$\int\limits^{3+cosθ } _{7cosθ } {rdr} \, dθ$                 [$θ=$θ ]

A=$2\int\limits^\frac{\pi }{3} _0$$[\frac{r^{2} }{2} ]^{7cosθ } }$dθ

A=$2\int\limits^\frac{\pi }{3} _0 {24cos^2θ-3cosθ-4.5 } } } \, dθ }$

A=[6sin2θ -3sinθ +7.5θ ]$\left \ {{\frac{\pi }{3} } \atop {0}} \right.$

A≈23.5

brainly.com/question/17255198

#SPJ4