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CENTROID OF SOLID REVOLUTION:

The region of the 1st quadrant which is bounded by the curve x^2 = 4y, the line x = 4, is revolved about the line x = 4, Locate the centroid of the resulting solid of revolution


1. Find the volume of the solid generated by revolving the region between the parabola


x = yΒ² + 1 and the line x = 3 about the line x = 3.


2. Find the area of the region bounded above by the curve 𝑦 = 2𝑒^βˆ’π‘₯ + π‘₯, below by the curve y =𝑒/π‘₯ 2, on the left by x = 0, and on the right by x = 1


Differentiate the trigonometric functions


1. = 2 sec x + tan x



2. y = sin x/ 1 + COS X



3. y = cos x cot x

Determine the real root of 𝑓(π‘₯)=π‘₯4βˆ’8π‘₯3βˆ’35π‘₯2+450π‘₯ βˆ’1001. Using false-position method to locate the root. Employ initial guesses of π‘₯l=4.5 and π‘₯u=6 and iterate until the estimated error πœ€a falls below the level of πœ€s=1.0%


Find the area of the region bounded by the curves x=yΒ³ and y=xΒ².

7. A cylindrical storage tank with a radius of 10 ft and a height of 30 ft is filled with water, which weighs approximately 62.4 Ib/ft3. Compute the amount of work performed by pumping the water up to a point 5 feet above the top of the tank.

6. A force of 20 lb stretches a spring from a natural length of 7 inches to a length of 12 inches. How much work was performed in stretching the spring to this length?

5. Suppose that a water tank is shaped like a right circular cone with the tip at the bottom, and has height 10 meters and radius 2 meters at the top. If the tank is full, how much work is required to pump all the water out over the top?

5. Suppose that a water tank is shaped like a right circular cone with the tip at the bottom, and has height 10 meters and radius 2 meters at the top. If the tank is full, how much work is required to pump all the water out over the top?

4. A spring has a natural length of 18 inches and a force of 201 lbs is required to stretch and hold the spring to a length of 24 inches. What is the work required to stretch the spring from a length of 21 inches to a length of 26 inches?

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