I have the attached graph, a part of a cosinusoidal curve (not sure if this is a correct translation). I don't have the function, but if I am correct: y = 3 cos (x*pi/2) The questions are: a) Calculate the area between that part of the curve and the x axis. b) Calculate the volume of the body created by rotating the part of the curve around the y axis. a) No problem here. P = 2 * integral from 0 to 1 of 3cos(xpi/2) dx I got the solution 12/pi. b) I got this far: To calculate the volume I need the area of the circles which constitute the body. To get that, I need to express x in terms of y. y = 3 cos (x*pi/2) arccos(y/3) = x*pi/2 x = (2/pi)arccos(y/3) The area is: P = x^2*pi So the volume is: V = integral from 0 to 3 of [(2/pi)arccos(y/3)]^2*pi dy Let I = integral of [(2/pi)arccos(y/3)]^2*pi dy I = integral of (4/pi)arccos^2(y/3) dy I = (4/pi) integral of arccos^2(y/3) dy substitute t = y/3, dt = dy/3, dy=3dt I = (12/pi) integral of arccos^2(t) dt I don't know how to integrate this. Anyone able to help?