Questions from General Calculus

Q: Evaluate the line integral ∫C F ∙ dr, where

Evaluate the line integral ∫C F ∙ dr, where C is given by the vector function r(t). F (x, y) = xy2 i - x2 j, r(t) = t3 i + t2 j, 0 < t < 1

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

Evaluate the line integral, where C is the given curve. ∫C (x/y) ds, C: x = t 3, y = t 4, 1 < t < 2

Q: (a). Show that the parametric equations x = a cosh

(a). Show that the parametric equations x = a cosh u cos v, y = b cosh u sin v, z = c sinh u, represent a hyperboloid of one sheet. (b). Use the parametric equations in part (a) to graph the hyperbolo...

Q: Evaluate the line integral ∫C F ∙ dr, where

Evaluate the line integral ∫C F ∙ dr, where C is given by the vector function r(t). F (x, y, z) = sin x i + cos y j + xz k, r (t) = t3 i - t2 j + t k, 0 < t < 1

Q: Evaluate the line integral ∫C F ∙ dr, where

Evaluate the line integral ∫C F ∙ dr, where C is given by the vector function r(t). F (x, y, z) = x i + y j + xy k, r(t) = cos t i + sin t j + t k, 0 < t < π

Q: Use a calculator to evaluate the line integral correct to four decimal

Use a calculator to evaluate the line integral correct to four decimal places. ∫C F ∙ dr, where F (x, y) = √(x + y) i + (y/x) j and r(t) = sin2 t i + sin t cos t j, π/6 < t < π/3

Q: (a). Find a parametric representation for the torus obtained by

(a). Find a parametric representation for the torus obtained by rotating about the z-axis the circle in the xz-plane with center (b, 0, 0) and radius a (b). Use the parametric equations found in part...

Q: Use a calculator to evaluate the line integral correct to four decimal

Use a calculator to evaluate the line integral correct to four decimal places. ∫C xy arctan z ds, where C has parametric equations x = t2, y = t3, z = √t, 1 < t < 2

Q: Find ∫∫S F ∙ n dS, where F (

Find ∫∫S F ∙ n dS, where F (x, y, z) = x i + y j + z k and S is the outwardly oriented surface shown in the figure (the boundary surface of a cu...

Q: Use a calculator to evaluate the line integral correct to four decimal

Use a calculator to evaluate the line integral correct to four decimal places. ∫C z ln (x + y) ds, where C has parametric equations x = 1 + 3t, y = 2 + t2, z = t4, -1 < t < 1