THEOREM 9.13 We now have the following theorem: The Area of a Region in the Polar Plane Bounded by a Function r = = f (0) Let a and ß be real numbers such that 0 ≤ B - a ≤ 27. Let R be the region in the polar plane bounded by the rays 0 = a and 0 = ß and a positive continuous function r = f(0). Then the area of region R is B 12 S (ƒ(0))² do. . 7 S 1 d 6. Explain how we arrive at the definite integral formula f(f(0))² do in Theorem 9.13 for computing the 1 HIN 2 2 area bounded by a polar function r = f(0) on an inter- val [a, b]. (Your explanation should include a limit of Riemann sums.) What would the integral ff(e) de represent?

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THEOREM 9.13
We now have the following theorem:
The Area of a Region in the Polar Plane Bounded by a Function r = = f (0)
Let a and ß be real numbers such that 0 ≤ B - a ≤ 27. Let R be the region in the
polar plane bounded by the rays 0 = a and 0 = ß and a positive continuous function
r = f(0). Then the area of region R is
B
12 S
(ƒ(0))² do.
.
Transcribed Image Text:THEOREM 9.13 We now have the following theorem: The Area of a Region in the Polar Plane Bounded by a Function r = = f (0) Let a and ß be real numbers such that 0 ≤ B - a ≤ 27. Let R be the region in the polar plane bounded by the rays 0 = a and 0 = ß and a positive continuous function r = f(0). Then the area of region R is B 12 S (ƒ(0))² do. .
7
S
1
d
6. Explain how we arrive at the definite integral formula
f(f(0))² do in Theorem 9.13 for computing the
1
HIN
2
2
area bounded by a polar function r = f(0) on an inter-
val [a, b]. (Your explanation should include a limit of
Riemann sums.) What would the integral ff(e) de
represent?
Transcribed Image Text:7 S 1 d 6. Explain how we arrive at the definite integral formula f(f(0))² do in Theorem 9.13 for computing the 1 HIN 2 2 area bounded by a polar function r = f(0) on an inter- val [a, b]. (Your explanation should include a limit of Riemann sums.) What would the integral ff(e) de represent?
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