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(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

  • integral -

    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

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