Questions from General Calculus

Q: Find the work done by the force field F (x,

Find the work done by the force field F (x, y, z) = 〈x - y^2, y - z^2, z - x^2 〉 on a particle that moves along the line segment from (0, 0, 1) to (2, 1, 0).

Q: The force exerted by an electric charge at the origin on a

The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = 〈x, y, z〉 is F (r) = Kr/|r |3 where K is a constant. (See Example 16.1.5.) Fin...

Q: The position of an object with mass m at time t is

The position of an object with mass m at time t is r(t) = at2 i + bt3 j, 0 < t < 1. (a). What is the force acting on the object at time t? (b). What is the work done by the force during the time inter...

Q: An object with mass m moves with position function r(t

An object with mass m moves with position function r(t) = a sin t i + b cos t j + ct k, 0 < t < y2. Find the work done on the object during this time period.

Q: A 160-lb man carries a 25-lb can of

A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with a radius of 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions climbing t...

Q: Evaluate the line integral, where C is the given curve.

Evaluate the line integral, where C is the given curve. ∫C y ds, C: x − t2, y = 2t, 0 < t < 3

Q: If C is a smooth curve given by a vector function r

If C is a smooth curve given by a vector function r (t), a

Q: Evaluate the line integral, where C is the given curve.

Evaluate the line integral, where C is the given curve. ∫C y2z ds, C is the line segment from (3, 1, 2) to (1, 2, 5)

Q: Evaluate the line integral, where C is the given curve.

Evaluate the line integral, where C is the given curve. ∫C xeyz ds, C is the line segment from (0, 0, 0) to (1, 2, 3)

Q: Evaluate the line integral, where C is the given curve.

Evaluate the line integral, where C is the given curve. ∫C (x2 + y2 + z2) ds, C: x = t, y = cos 2t, z = sin 2t, 0 < t < π2