Question 4 The figure above shows the graphs of the polar curves r = 2sin² 0 and r = 4sin2 0 for 0 ≤ 0 ≤ T. Which of the following integrals gives the area of the region bounded between the two polar curves? S (В (с D sin²0d0 S. 2sin²0d0 2sin¹0d0 S." +X 6sin¹0d0
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- Given the graphs of polar equations: r=1 and r=−2cosθ, (a) Set up the integral that gives the area of the shaded region. (b) Evaluate the area of the region showing all your steps.Two polar curves C1 and C2 is given in the interval 0 ≤ θ ≤ θ ≤ π/4 r = sqrt(2) *cos(2θ) and r = sqrt(4θ) Find the area within C1 and C2Fast pls solve this question correctly in 5 min pls I will give u like for sure Mnty Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant between the circles x^2+y^2=144 and x^2-12x+y^2=0
- 1. Consider the area enclosed between the circle x^2 + y^2 = 4, the line y = 3, y = x, and y = -x (b) Draw the curves on the graph below and shade the described region. (c) Set up a single polar integral that computes the area of the shaded region and find the area of the shaded region.The graphs of the polar curves r=5 and r=5+2sin(3ø) are shown in the figure for 0 is less than or equal to ø is less than or equal to 2 pi. Let R be the area of the shaded region inside the graph of r=5 and inside the graph of r=5+2sin(3ø) from 0 is less than or equal to ø is less than or equal to pi. Write an integral expression for the area of R.II. Consider the circle C1 : r = 1 and the roses C2 : r = cos 2θ and C3 : r = 2 cos 2θ, each of which is symmetric with respect to the polar axis, the π/2-axis, and the origin, as shown on the image. 1. Find polar coordinates (r, θ) for the intersection A of C1 and C3, where r, θ > 0. 2. Set-up (do not evaluate) a sum of three definite integrals that give the perimeter of the yellow-shaded region inside both C1 and C3 but outside C2. 3. Find the area of the unshaded region inside C3 but outside C1.
- Find an iterated integral in polar coordinates that represents the area of the given region in the polar plane and then evaluate the integral. One loop of the curve r = 4 sin3θ.Fast pls solve this question correctly in 5 min pls I will give u like for sure Sini find the surface area of the part of the paraboloid z=x^2+y^2 that lies between the planes x = 1 and x = 4.Let C1 be the circle r = 3 cos θ and C2 the cardioid r = 1 + cos θ.(a) Find all point(s) of intersection of the two given polar curves. (b) Set up an integral for the perimeter of the shaded region. No need to evaluate.(c) Set up an integral for the area of the shaded region. No need to evaluate. Show necessary steps and process.
- draw a sketch of the plane region then solve the problems as instructed. Set up and evaluate the required integral to solve the problem, express your answer in the exact form in fraction, in terms of e, ln , π, etc. (not in decimal).Use the integration capabilities of a graphing utility to approximate the area of the region bounded by the graph of the polar equation. r = 2/(7 − 6 sin)Sketch the graph of the cardioid r = 1 + cosθ and the circle r = 3cosθ. Shade the region that is inside of the cardioid and inside of the circle. Set up the integral for: a) the perimeter of the shaded region b) the area of the shaded region .