Calculus Answers

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

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?

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?

3. A force of F(x)=x²-cos(3x) +2, x is in meters, acts on an object. What is the work required to move the object from x=3 to x=7?

3) Solve the area bounded by the curve y = 4x-x and the lines x = -2 and y = 4.

2) Find the area bounded by the curve x = y² + 2y and the line x = 3.

1) Find the area bounded by the curve y-9-x and the x axis.

a) Horizontal Strip

b) Vertical Strip