posted by matrix school 2 .
(1) The region in the x-y plane bounded by the curve y=x^2, the line x=0 and the line x=5 and the x-axis. find the volume generated
(2) Assume that a force of (3x^2-x+1)N is pulling an object at each point of the x-axis. find the work done in moving the object from x=1 to x=4
1) THE differential area dA will be y dx or x^2 dx, integrated from x=0 to 5. Now integrate that around the x axis, by rotation. Area=INT Area dTheta where theta runs from 0 to 2PI
2) Work= INT force dx
= INT(3x^2-x+1)dx from x=1 to 4