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- 1. Find the volume of the solid of revolution generated by revolving the region bounded by the graphs of y = ex, y = 0, x = 0, and x = 2 around the line y = -1.Consider the region bounded by the graphs of y = sin-1 x, y = 0,and x = 1/2. Find the centroid of the region.Since the R integration region is the region bounded by the hyperbolas x2 - y2 = 1, x2 - y2 = 9, xy = 4 and xy = 2 in the first region, with the help of u = xy and v = x2 - y2 transformation ∫∫R ( x2 + y2) dA What is the value of the integral?a) 0b) -7c) 7d) 8e) none
- The first quadrant area bounded by y2=8x, x=2 and y=0 is revolved about the x-axis. Find the centroid of the solid revolution.Question #19.Find the centroid of the region bounded by the graphs of y=x,x=1/y^2 and y=28.2) 5) The given curve is rotated about the yaxis. Set up, but do not evaluate, an integral for the area of the resulting surface by inte grating (a) with respect to x and (b) with respect to y.
- R is a region on the quadrilateral having vertices (2,3), (2,5), (0,1) and (0,3). S, on the other hand, is a plane with equation 48 = 16x + 8y + 2z. Set up its iterated double integral, which is equal to the volume below S and above R, and solve for the area of the portion of S above region R.3. Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region and the solid formed. y= x², x=y² ; about x= -12. SET UP ONLY: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs of y = (x-2)1/2, y = 0, and x = 4 around the line x = -3