Y in the plane b using the fundamental theorem of

Info iconThis preview shows pages 4–7. Sign up to view the full content.

View Full Document Right Arrow Icon
y ) in the plane. (b) Using the Fundamental Theorem of Line Integrals, evaluate the path integral below, where C is any smooth path from the origin to the point ( π /2,ln(2)). [ WARNING: You must use the theorem to get credit here.] ______________________________________________________________________ 8. (18 pts.) Write down but do not attempt to evaluate the iterated triple integrals in (a) rectangular, (b) cylindrical, and (c) spherical coordinates that would be used to compute the volume of the sphere with a radius of 1 centered at the origin. [For rectangular, there are many correct variants.] (a) V = (b) V = (c) V =
Background image of page 4

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Name: Final Exam/MAC2313 Page 5 of 7 ______________________________________________________________________ 9. (12 pts.) Let . Compute the divergence and the curl of the vector field F . (a) div F = (b) curl F = ______________________________________________________________________ 10. (16 pts.) Use the substitution u = x + y , v = x - y to evaluate the integral where R is the region enclosed by the lines x + y = 0, x + y = 1, x - y = 1, and x - y = 4
Background image of page 5
Name: Final Exam/MAC2313 Page 6 of 7 ______________________________________________________________________ 11. (12 pts.) A particle, starting at (0,0) moves to the point (1,1) along the parabola y = x 2 and then returns to (0,0) along the parabola x = y
Background image of page 6

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page4 / 7

y in the plane b Using the Fundamental Theorem of Line...

This preview shows document pages 4 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online