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- A flat circular plate has the shape of the region x2 + y2<= 1. The plate, including the boundary where x2 + y2 = 1, is heated so that the temperature at the point (x, y) is T(x, y) = x2 + 2y2 - x. Find the temperatures at the hottest and coldest points on the plate.a. Find the area bounded by the curves y=-x^2+4, and y = 0. b. Find the volume generated by revolving the area enclosed by the curve x^2 + y^2 = 36 about the y-axis. c. Find the volume generated by revolving the area bounded by the lines x + 2y = 4, x =0 and y = 0, about x-axis.Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra system to confirm your results. f(x, y) = x2 + 2xy + y2, R = {(x, y) : |x| ≤ 7, |y| ≤ 3} (x, y, z) = ( ) (smallest x-value) (x, y, z) = ( ) (largest x-value) y = absolute minimum
- 2) the region bounded by y= x+2, y=x^2 revolve about the line y=5 find the region bounded relvoving around the y axisPlate with variable density Find the mass and first momentsabout the coordinate axes of a thin square plate bounded by thelines x = ±1, y = ±1 in the xy-plane if the density is d(x, y) =x2 + y2 + 1/3.Let S be the solid of revolution obtained by revolving about the x-axis the bounded region R enclosed by the curve y=e−2x and the lines x=−1, x=1 and y=0. We compute the volume of S using the disk method. a) Let u be a real number in the interval −1≤x≤1. The section x=u of S is a disk. What is the radius and area of the disk? Radius: Area: b) The volume of S is given by the integral (b to a) ∫f(x)dx, where: a= b= and f(x)= c) Find the volume of S. Give your answer with an accuracy of four decimal places. Volume:
- volume of the solid generated when the region bounded by y = 9 − x2 and y = 2x + 6 is revolved about the x-axis.z2=y2+x2 cone and x2+y2= 4 calculate the volume of Solid ''S'' bounded by its cylinder My mother tongue is not English so I cannot always read handwriting please write clearly and nicely or in computer script thank youRegion bounded by: y=1/2x, x=2, x=4. y=0 Rotate about x-axis. Find the area
- Work through all integrals. Determine the volumes of the solids of revolution generated by revolving the given region about the given line. Do by the method indicated. - The region bounded by y = x^2 , y = 2x, is revolved about the y axis. Do by shell method and washers.triple integral of function x8ey bounded by z=4-y^2 and planes z=0, x=2, and x=-2find the volumes of the solids generated byrevolving the regions about the given axes. If you think it would bebetter to use washers in any given instance, feel free to do so. The region in the first quadrant bounded by the curve x = y - y3and the y-axis about the x-axis