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Find the mass of the thin bar with the given density functionρ(x) = 2 + x2;  for 0 ≤ x ≤ 1

Solve the problem.Find a curve through the point  whose length integral, 1 ≤ x ≤ 2, is 

Find the length of the curve.x = (y – 1) 3/2 from y = 4 to y = 9

Find the mass of the thin bar with the given density functionρ(x) = 3 + x2;  for 0 ≤ x ≤ 1

Find the area of the surface generated when the given curve is revolved about the x-axis.  y = 2x + 5 on [0, 5]

Find the derivative of y.y = sinh2 7x

Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the . y = x2 + 3, y = 2x + 3

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.y = 8×2, y = 8

Solve the problem.A spring on a horizontal surface can be stretched and held 0.5 m from its equilibrium position with a force of 50 N. How much work is done in stretching the spring 3 m from its equilibrium position?

Find the area of the surface generated when the given curve is revolved about the x-axis.  y =   on