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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  

Use a calculator to approximate the area of the surface generated when the given curve is revolved about the x-axis. Round to two decimal places when necessary.y = x8  on [0, 1]

Solve the problem.A cylindrical water tank has height 10 m and radius 2 m (see figure). If the tank is full of water, how much work is required to pump the water to the level of the top of the tank and out of the tank? Express the answer in terms of π. 

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines.y = 2x,y = x2; revolve about the y-axis

Write the integral that gives the surface area generated when the curve is revolved about the x-axis. Do not simplify.y = ln x4  on [1, ]

Find the volume of the described solid.The solid lies between planes perpendicular to the x-axis at  and . The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola  to the parabola .