Questions from General Calculus

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

Evaluate the line integral, where C is the given curve. ∫C xy4 ds, C is the right half of the circle x2 + y2 = 16

Q: (a). Evaluate the line integral∫C F ∙

(a). Evaluate the line integral∫C F ∙ dr, where F (x, y, z) = x i - z j + y k and C is given by r(t) = 2t i + 3t j - t2 k, -1 (b). Illustrate part (a) by using a c...

Q: Find the exact value of ∫C x3y2z ds, where C

Find the exact value of ∫C x3y2z ds, where C is the curve with parametric equations x = e-t cos 4t, y = e-t sin 4t, z = e-t, 0 < t < 2π.

Q: A thin wire is bent into the shape of a semicircle x2

A thin wire is bent into the shape of a semicircle x2 + y2 = 4, x > 0. If the linear density is a constant k, find the mass and center of mass of the wire.

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

Evaluate the line integral, where C is the given curve. ∫C xey ds, C is the line segment from (2, 0) to (5, 4)

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

Evaluate the line integral, where C is the given curve. ∫C (x2y + sin x) dy, C is the arc of the parabola y = x2 from (0, 0) to (π, π2)

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

Evaluate the line integral, where C is the given curve. ∫C ex dx, C is the arc of the curve x = y3 from (-1, -1) to (1, 1)

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

Evaluate the line integral, where C is the given curve. ∫C (x + 2y) dx + x2 dy, C consists of line segments from (0, 0) to (2, 1) and from (2, 1) to (3, 0)

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

Evaluate the line integral, where C is the given curve. ∫C x2 dx + y2 dy, C consists of the arc of the circle x2 + y2 = 4 from (2, 0) to (0, 2) followed by the line segment from (0, 2) to (4, 3)

Q: Investigate the shape of the surface with parametric equations x = sin

Investigate the shape of the surface with parametric equations x = sin u, y = sin v, z = sin (u + v). Start by graphing the surface from several points of view. Explain the appearance of the graphs by...