(3x{y4 – 6xy)dx + (4.x® y3 – 3x²)dy, where C is any path 13. Evaluate the...
2. Evaluate the line integral / (x+2y)dx + r’dy, where C consists of the path C from (0,0) to (3,0), the path C2 from (3,0) to (2,1), and the path C3 from (2,1) to (0,0) by applying the following steps. (a) Evaluate (x + 2y) dx + c'dy, by parametrizing C C (b) Evaluate [ (x + 2y)dx + x>dy, by parametrizing C, (c) Evaluate | (x + 2y)dx + x’dy, by parametrizing C3 (d) Evaluate (+2y)dx + xºdy
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
c) fox2y2 dx - xy3 dy, where C is the triangle with vertices (0, 0), (1, 0), (1, 1). (CE. Lect 08) Our goal is to evaluate the line integral in No. 3 (c), p. 279 of Kaplan (the last part of this question). The path involved is a triangle. To calculate such a line integral, we break up its path into pieces (hence the first three parts of this question). At the end, we add the pieces together. (a)...
Apply Green's Theorem to evaluate the integral. froy 1 + x)dx + (y + 3x)dy C: The circle (x - 7)2 + (y – 5)2 = 5 с froy + x)dx + (y + 3x)dy = с Tyne an eyact answer using as needed
The differential equation4xy²+6xy+(4x²y+3x²+1)dy/dx=0Has solutions of form F(x, y)=c whereF(x, y)= _______
Evaluate the line integral. fr de x² dx + y²dy, where C is 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).
(5,3,-2) Evaluate the integral y dx + x dy + 4 dz by finding parametric equations for the line segment from (2,1,5) to (5,3,-2) and evaluating the line integral of (2,1,5) F = yi + x3 + 4k along the segment. Since F is conservative, the integral is independent of the path. (5,3,-2) y dx + x dy + 4 dz= (2,1,5)
score: 0 of 1 pt X 15.1.6 Evaluate the iterated integral. || (x?y-9xy) dy dx S S (x+y=9xy) dy dx= [(Type an integer or a simplified fraction.) Homework: Section 15.1 Matt Score: 0 of 1 pt X 15.1.9 Evaluate the iterated integral. In 2 In 5 3x + 24 dy dx 0 1 In 2 In 5 3x + 2y dy dx = (Type an exact answer.) ints Homework: Section Score: 0 of 1 pt X 15.1.10 Evaluate the iterated...
4) Use a potential function to evaluate the line integral. The integral is path independent. S. (2xy2 + y®)dx + (x^2 +2y2 + 2xy) dy+(x2y + yº) da, y(t) = (1+0,7%, (1 - 2)e'), 05152
(1 point) Show that the line integral 2xe-y dx + (4y – xey) dy is independent of path 0Q - M Evaluate the integral ( 2xe”) dx +(4y= xe=") dy = where C is any path from (1,0) to (3, 1).