Find the area of the region that is bounded by r = sin 0 + cos 0, with 0 <OST. Find the area of the right half of the cardioid: r = 1 + 3 sin .
* 2. Find the area of the region bounded by the graphs of r = 3 - y2 and y=r-1, integrating (a) with respect to y; (b) with respect to r.
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)
and the r-axis. 5. Consider the region S bounded by r 1, r = 5, y (a) Use four rectangles and a Riemann sum to approximate the area of the region S. Sketch the region S and the rectangles and indicate your rectangles overestimate or underestimate the area of S. (b) Find an expression for the area of the region S as a limit. Do not evaluate the limit.
and the r-axis. 5. Consider the region S bounded by r...
Find the area of the region bounded by the curves r = 2 + cos(2), 0 = 0, and = /4. You may need the formulas: cos” (a) = 1+ cos(22), sin?(x) = 1 – cos(22)
Find the area S of the surface that is formed by revolving the region bounded by the graph of y= 22 + 2 on the interval (0, 2) about the Z-axis. Select one: e a. None of these O b. S = 1657 Oo. S = 5737 O d. S=2757
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1. Consider the region R bounded by the graph of y 0, 7Tand the x-axis sin() on a) Find the area of R b) Find the volume of the solid of revolution obtained by rotation of R about the x-axis c) Find the volume of the solid of revolution obtained by rotation of R about the y-axis d) Find the coordinates of the center of mass of R
1. Consider...
Solve 1A & 1B 1A) Find the area of the region that is bounded by the given curve and lies in the specified sector. r = θ2, 0 ≤ θ ≤ π/6 1B) Find the area that r = 1 + sin(4θ) encloses.
Find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval [-21/3, 31/4]. The area is (Type an exact answer, using radicals as needed.)
Find the area of the region described below. The region bounded by y = 3x2 and y=x? +2 The area of the region is . (Type an integer or a simplified fraction.)