A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write f(x, y) dA as an iterated int -1 f(r cos(8), r sin(0))r dr de f(x, y)x dy dx (x+ 1)/2 f(r, e)r dr de f(x, y) dy dx x+1)/2

Q: Determine the area in the first quadrant bound by the polar function r(0) = sin (0) – 1.

A: Here, since the area is in the first quadrant, we can calculate the area with the help of integral…

Q: State the formula for the Area of the sector bounded by a polar curve r = f (θ ) and two rays θ = α…

A: Given: The equation of polar curve is: r=fθ where, α≤θ≤β

Q: Find the Jacobian for the change of variables defined by x = r cos θ and y = r sin θ.

A: To calculate the Jacobian for the change of variables, we need to calculate the following…

Q: Q1) Evaluate the integral dy dx using polar coordinate

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Q: Calculate the area of the circle r = 3 sin θ bounded by the rays θ = π/3 and θ = 2π/3.

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Q: O Find plane area inside the polar function r = 2 and outside polar function r = 2 sin (+ 0) in…

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Q: Find the area of the region lying below the x-axis and above the polar curve r = 1 + sin(0).

A: Given polar curve is: r=1+sinθ To find: Area of the region lying below the x-axis and above the…

Q: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

Q: convert the region xy > 0 to polar coordinates

A: The objective of the question is to convert the given region in Cartesian coordinates (xy > 0) to…

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: Sexyz ds, C: x= 2 sin t, y = t, z= -2 cos t, 0sts T

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Q: Evaluate F dr where C is the line segment from (7,-,1) to (20, 1, and F (sin(yz) + 1)i + (zz cos(yz)…

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Q: 1 @[₁ 1. Use polar coordinates to evaluate -1 JO /1-x² (x² + y²)³/2 dy dx.

A: By using polar coordinates to evaluate the following integral.