Questions from General Calculus

Q: How do you use power series to solve a differential equation?

How do you use power series to solve a differential equation?

Q: Evaluate the line integral. ∫C √xy dx +

Evaluate the line integral. ∫C √xy dx + ey dy + xz dz, C is given by r (t) = t4 i + t2 j + t3 k, 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 xyeyz dy, C: x = t, y = t2, z = t3, 0 < t < 1

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

Evaluate the line integral, where C is the given curve. ∫Cy dx + z dy + x dz, C: x = √t, y = t, z = t2, 1 < t < 4

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

Evaluate the line integral, where C is the given curve. ∫C z2 dx + x2 dy + y2 dz, C is the line segment from (1, 0, 0) to (4, 1, 2)

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

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

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 + y2) i + xz j + (y + z) k, r(t) = t2 i + t3 j - 2t k, 0 < t < 2

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, z) = yzex i + zxey j + xyez k and r(t) = sin t i + cos t j + tan t k, 0 < t < π/4

Q: Use Green’s Theorem to evaluate the line integral along the given positively

Use Green’s Theorem to evaluate the line integral along the given positively oriented curve. ∫C (1 - y3) dx + (x3 + ey 2) dy, C is the boundary of the region between the circles x2 + y2 = 4 and x2 +...

Q: Use Green’s Theorem to evaluate ∫C F ∙ dr.

Use Green’s Theorem to evaluate ∫C F ∙ dr. (Check the orientation of the curve before applying the theorem.) F (x, y) =〈y cos x - xy sin x, xy + x cos x〉, C is the triangle from (0, 0) to (0, 4) to (...