uneskovogl5
2021-11-16
Answered

Find the area of the region enclosed by one loop of the curve. $r=\mathrm{sin}4\theta$

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Annie Midgett

Answered 2021-11-17
Author has **7** answers

Step 1

Area enclosed by one of the loops will be simply

We will find the limits of integration a, b, and then we will integrate the integral to find the area enclosed by one of the loops.

To find the limits of integration, we need to find two consecutive values of

Graph of

We can see that 0 and

Therefore, we can integrate from 0 to

You can also integrate from

The only condition is that you have to integrate between two consecutive values of

Step 3

Therefore, the limit of integration is from 0 to

Area enclosed by one of the loops is

We used the formula

Area enclosed by the loop is

Philip O'Neill

Answered 2021-11-18
Author has **8** answers

Step 1

The given curve is

Area of the curve enclosed in the first loop is,

Step 2

Two consecutive value of theta for which

Step 3

Now integrate from 0 to

Area enclosed by one of the loop is,

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