Y r = 4 sin 0 r = 1+ sin 0 B 2. Consider the polar curves (see figure above) r = 1+ sin 0 and r = 4 sin 0. (a) Compute the exact polar coordinates of the intersection points A and B. (b) Determine the exact area of the region that lies inside r = 1+ sin 0 and outside r = 4 sin 0 in the right half plane.
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- Use the integration capabilities of a graphing utility to approximate the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 4 cos 2θ, [0, π/ 4]2. Consider the polar curves r = 4 - 2cosθ and r = 2 + 2cosθ. In this problem, we want to find the area of A, B, and C pictured below. (c) B is the area inside both r = 2 + 2cosθ and r = 4 - 2cosθ. Find the area of B. (Hint: What happens at the angle where the two polar curves intersect? Your answer should involve a sum of two polar integrals.)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.
- 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)Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu Integrate f (x, y) = y over the top half of the circle (x − 1)2 + y2 = 1 in two ways a) In rectangular coordinates. b) In polar coordinatesConsider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface area of the solid obtained by rotating the region about the x-axis.
- Find the area of the region which is inside the polar curve r=3cos(theta) and outside the curve r=2-1cos(theta)Find the surface area resulting from the rotation of the parts in the first and fourth quadrants of the polar curve r = 1 - cos(θ) around the line θ=π/2, formulate only the necessary integral without solving it. Please solve a question quickly I need this Answer at half time Quickly. Please(a) Find the exact area of the surface obtained by rotating the curve y = e^x about thex-axis over the interval 0 ≤ x ≤ 1.(b) Determine the length of the parametric curve given by the following set ofparametric equations.x = 3 cos t − cos 3t, y = 3 sin t − sin 3t, 0 ≤ t ≤ πYou may assume that the curve traces out exactly once for the given range of t.
- 1) Represent I with the ordered of integration dydx 2) Represent I using polar coordinatesUse a graphing utility to graph the polar equation over the given interval. Use the integration capabilities of the graphing utility to approximate the length of the curve. r = eθ, [0, π]When we investigated area in rectangular coordinates in Chapter 4, we often tried to find the areas of regions under curves y = f(x) from x = a to x = b. In the polar plane, the typical region whose area we wish to find is a region R bounded by two rays θ = α and θ = β and a polar function of the form r = f(θ). Why is this our basic type of region in the polar plane?