Calculus Answers

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 = y² + 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^−𝑥 + 𝑥, below by the curve y =𝑒/𝑥 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(𝑥)=𝑥⁴−8𝑥³−35𝑥²+450𝑥 −1001. Using false-position method to locate the root. Employ initial guesses of 𝑥_l=4.5 and 𝑥_u=6 and iterate until the estimated error 𝜀_a falls below the level of 𝜀_s=1.0%

Find the area of the region bounded by the curves x=y³ and y=x².

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?