(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)...
The differential equation4xy²+6xy+(4x²y+3x²+1)dy/dx=0Has solutions of form F(x, y)=c whereF(x, y)= _______
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
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).