Let S be the region in the first quadrant bounded above by the graph of the polar curve r = cos θ and bounded below by the graph of the polar curve r= 20, as shown in the figure above. The two curves intersect when θ = 0.450. What is the area of S?
(A) 0.232 (B) 0.243(C) 0.27 (D) 0.384
Let S be the region in the first quadrant bounded above by the graph of the polar curve r = cos θ...
5. The graphs of the polar curves r-4 and r-3 + 2 cos θ are shown in the figure above. The curves intersect 3 (a) Let R be the shaded region that is inside the graph of r-4 and also outside the graph of r 34 2 cos θ, as shown in the figure above. Write an expression involving an integral for the area of R. (b) Find the slope of the line tangent to the graph of r :-3...
Let R be the region shown above bounded by the curve C = C1[C2. C1 is a semicircle with center at the origin O and radius 9 5 . C2 is part of an ellipse with center at (4; 0), horizontal semi-axis a = 5 and vertical semi-axis b = 3. Thanks a lot for your help:) 1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
Let R be the region inside the graph of the polar curver=3 and outside the graph of the polar curve r=3(1 - cos 6). (a) Sketch the two polar curves in the xy-plane and shade the region R. (b) Find the area of R.
Let R be the first quadrant region bounded by the lines y = x, y = 4x, and the hyperbolas xy = 1 and xy = 4. Calculate the area of R
Let R be the region in the first quadrant bounded by the x-axis and the graphs of y = in(x) and y=5-x, as shown in the figure above. a) Find the area of R. b) Region R is the base of a solid. For the solid, each cross-section perpendicular to the x-axis is a right isosceles triangle whose leg falls in the region. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid. c)...
2) The region R in the first quadrant of the xy-plane is bounded by the curves y=−3x^2+21x+54, x=0 and y=0. A solid S is formed by rotating R about the y-axis: the (exact) volume of S is = 3) The region R in the first quadrant of the xy-plane is bounded by the curves y=−2sin(x), x=π, x=2π and y=0. A solid S is formed by rotating R about the y-axis: the volume of S is = 4) The region bounded...
(10 points) Let R be the region in the first quadrant bounded by the x and y axes and the line y = 1 – 1. Notice R is a triangle with area 1/2 (you do not need to verify this). Find the coordinate of the centroid of R. For extra credit, determine the y coordinate without calculating an integral. (Note: If we regard R as a plate, then the centroid of R can also be thought of as the...
The region inside the curve r= 4 cos θ and outside the curve r = 2. r(t) 2 rt)4cos(t) -1 What are the coordinates of the point where the two circles intersect at the top of the picture in terms of (r,0) What are the coordinates of the same point in cartesians coordinates (x.y)? Give an equivalent version of the point in polar coordinates with r <o. What is the slope of of the tangent line to the circler 2...
The region R in the first quadrant bounded by the curve y = x2 + 1 and the line y = 3x + 1 is revolved about the line y = 1. SKETCH the solid of revolution and find its VOLUME by i) The Washer Method ii) The Shell Method
Calculus Find the centroid of the region in the first quadrant bounded by the given curves. y = x4, x=yt (3, 3) = ( A vertical dam has a semicircular gate as shown in the figure. The total depth d of the figure is 14 m, the height h of air above the water level is 2 m, and the width w of the gate is 2 m. Find the hydrostatic force against the gate. (Round your answer to the...