I need help with these; for the last two attachments please also sketch the solid, and a typical disk or washer in addition to the region.

Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y = x, x= y; about y = 1 V = Sketch the region.Find the volume V of the solid obtained by rotating the region bounded by the graphs of the given expressions about the specified line. y = 27x', y = 0, x=1; about x = 2 V Sketch the region.Let R be the region bounded by the graphs of f(x) = v x, g(x) = 6 - x, and the x-axis. Which of the following expressions gives the volume of the solid generated when R is rotated about the y-axis? On (6 - x) 2 - (x2 ) 2 ] dy On (6 - y - v 2)2 dy On (6 - y)2 dy - 3614 dyLet R be the region in the rst quadrant bounded by the y-axis and the graphs of y = x2 + 1 and y = 9 ex. (a) Find the area of the region R. (Round your answer to three decimal places.) (b) Find the volume of the solid that results when R is rotated about the x-axis. (Round your answer to three decimal places.) (c) The solid 5 has base R. Each cross-section perpendicular to the x-axis is a semicircle whose diameter lies in R. Find the volume of the solid 5. (Round your answer to three decimal places.) (d) The vertical line x = k divides the region R into two regions of equal areas. Write, but do not solve, an equation involving one or more integral expressions that could be used to determine the value of k. (Let a represent the x coordinate of where the graphs intersect.) O /a(9ex)dx=/a(x2+1)dx k k O[kwex)(x2+1)dx=/a(9eX)(x2+1)dx 0 k 0]! k(9ex)Z(X2+1)de=7r a(9ex)2(x2+1)2dx k 0 a k 0/ (9eX)(x2+1)dx=/ (9eX)(x2+1)dx 0 0 k k O/(Sex)dx=/ (x2+1)dx fl n