1. Compute dr + (1²y3) dy where C is the curve below. (Hint: try using Green's...
se Green's theorem in order to compute the line integral ∮C(ex2−y3)dx+(sin(y3)+x4)dy∮C(ex2−y3)dx+(sin(y3)+x4)dy where CC is the boundary of the square [0,1]×[0,1][0,1]×[0,1] traversed in the counterclockwise way.
A. Fundamental theorem of line integrals
B. Green's Theorem
c. Parameterize the curve and compute the line integral
long-hand
D. none of the above, problem cannot be solved
Consider the line integral (el + cos x + y) dx + +yey + dy where C is the curve pictured below. 2 (-1,-3) (3,-4) Identify the best approach to doing this problem:
Let R be the region shown above bounded by the curve C = C1[C2.
C1 is a semicircle with center
at the origin O and radius 9
5 . C2 is part of an ellipse with center at (4; 0), horizontal
semi-axis
a = 5 and vertical semi-axis b = 3.
Thanks a lot for your help:)
1. Let R be the region shown above bounded by the curve C - C1 UC2. C1 is a semicircle with centre at...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove İ}!").lx (ly İ)(2 dr dy. Pdr+Qdy That is, prove Green's Theorem for the triangle A. [Hint: the lecture notes have a proof for when A is a rectangle. So, the idea is is to give a similar proof where we have this...
14. Use Green's theorem to evaluate the line integral Sc 2xy3dx + 4x2y2 dy where Cis the boundary of the triangular" region in the first quadrant enclosed by the x-axis, the line x-1, and the curve y=x3.
Evaluating using Green's theorem
(4x^3+sin(y^2))dy-(4y^3+cos(x^2))dx where C is the boundary of the
region x^2+y^24
Please be detail thanks.
We were unable to transcribe this image3. EVALUATE USING GREEN'S THEOREM (4x++sinyydy –(4y+cosx2) dx, WHERE C IS THE BOUNDARY OF THE REGION X+Y24.
Evaluate the following integrals using Green's theorem. 8. S. (2y2 + xsin(x)dx + (x3 - evy)dy where c is the rectangle in R2 with vertices at (1,0), (2,0), (2,2) and (1,2) oriented counterclockwise.
evaluate using green's theorem line integral (4x^3+sin y^2)dy-(4y^3+cosx^2)dx, where C is the boundary of the region x^2+y^2 greater equal to 4
2. Use Green's theorem in order to compute the line integral $ (x - 1)3 dy - (y-2): d.x where C is the circle of radius 3 centered at (1, 2) and traversed in the counterclockwise way.
13. Use Green's Theorema to evaluate S (1+tan y)dx+(+ev)dy where C is the positively oriented boundary of the region enclosed by y=, x= n/6 and y=0. (A) -2- 1 (B) 2 - 1 (C) 2+ 2 (D) 2 - 7 (E) none of these