Question
Asked Oct 31, 2019
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Find the area of the region that is bounded by the given curve and lies in the specified sector.

4. r = 1/θ,    (pi/2) <= θ <= 2pi

10.4 EXERCISES
1-4 Find the area of the region that is bounded by the given
curve and lies in the specified sector.
1. r = e 0/4, TT/2 0T
2. r cos 0, 00T/6
i6
us s
3. r= sin 0 + cos 0, 0 <0 < T
4. r 1/0, T 2 02T
6
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10.4 EXERCISES 1-4 Find the area of the region that is bounded by the given curve and lies in the specified sector. 1. r = e 0/4, TT/2 0T 2. r cos 0, 00T/6 i6 us s 3. r= sin 0 + cos 0, 0 <0 < T 4. r 1/0, T 2 02T 6

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Expert Answer

Step 1

We have to use area formula of polar coordinates with a= pi/2 and b=2pi

b
A= de
2
2
A=
2
2
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b A= de 2 2 A= 2 2

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Step 2

We plug r=1/theta in the formula and then try to integ...

S
2
A=
2
r
1
A=
2
2 1
OP
2
2
A=
2
2T
A= -
2
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S 2 A= 2 r 1 A= 2 2 1 OP 2 2 A= 2 2T A= - 2

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