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?

Q: Express the region D = {(x, y)|3x² + 3y² ≤ 45} in polar coordinates.

A: D=x,y|3x2+3y2≤45

Q: 5) Find the area of the region bounded by the following function using the polar form f(8) = r =…

A:

Q: ) Evaluate √x² + y²dA where D is the region bounded by the polar curve r = 2 cos. Sketch the region.…

A:

Q: Determine the image of the set of points |z| =3, -\pi/4 <=θ <= 3pi/4 under the reciprocal…

A: Step 1:Given that ∣z∣=3⟹z=3eiθ,−4π​≤θ≤43π​ Step 2:Now the reciprocal mapping is…

Q: B D (4+3+5+2) (1+16+9+25) O (16+9+25+4) 0=1 L 0 T 0 1 ļ 4 ! 3 0=0 3 r = f(0) 5 Let R be the region…

A: Given: In the region R we have, θ 0 14 12 34 1 r 1 4 3 5 2 To Find: The approximate area of…

Q: 5) Using the definition of the contour integral compute the integral of f(z) = 1+i-22 from Zo =0 to…

A: Given that we have to calculate

Q: Use polar coordinates to evaluate || (2x-3y) dA, R ere R is the region in the upper half-plane…

A: Consider the given information.