EQuestion Help 15.4.23 Use the Green's Theorem area fomula, Areyy dk o fnd he area of the region,...
please answer all 3 questions, I need help. thank you Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(9x+ ex) dy- (4y + sinh x) dx, where C is the boundary of the square with vertices (2, 0), (5, 0), (5, 3), and (2, 3). $(9x+ ey?) ay- (4y+ + sinhx) dx = 0 (Type an exact answer.) Use Green's Theorem to evaluate the following line integral. i dy - g dx, where (19)...
7.2.66 Use the substitution fomula to evaluate the integral. 0 e*dx 1+ e 13 0 e Xdx 3 3 (Type an exact answer, using π as needed.) enkos.. ironm
Evaluate the line integral in Stokes Theorem to evaluate the surface integral J J(VxF)-n ds. Assume that n points in an upward direction F (xty,y z,z+x) S is the tilted disk enclosed by r()-(3 cost,4sint,7 cos t Rewrite the surface integral as a line integral. Use increasing limits of integration. dt (Type exact answers, using π as needed.) Find the value of the surface integral. JÍs×F).nds-ロ (Type an exact answer, using π as needed.) Evaluate the line integral in Stokes...
Find the total area of the shaded region. The total area of the shaded region is 1 (Type an exact answer, using * as needed.) Ay y2 y-200x²x R/2 3/2 2x
2. EXTRA CREDIT OPTION: GREEN'S THEOREM Fix θ > 0, Consider the region A bounded by the straight line segment from (0,0) to (1,0), the portion of the hyperbola parametrized by r(t) (cosh(t), sinh(t)) for 0 t 0, and the straight line segment from P-(cosh(9), sinh(9) back to the origin. Using the vector field F-1/2(-y,z) and Green's Theorem, find the area of A in terms of θ. Show all work in an organized, well-written manner for full credit. 2. EXTRA...
Find the area of the following region. The region inside limaçon r= 6-4 cos e The area of the region bounded by r= 6-4cos o is (Type an exact answer, using it as needed.) square units.
. Find the area of the entire region The intersection points of the following curves are (0,0) and that lies within both curves. r= 18 sin 0 and r= 18 cos | The area of the region that lies within both curves is (Type an exact answer, using a as needed.) Find the area of the region common to the circle r=5 and the cardioid r=5(1 - cos 0). The area shared by the circle and the cardioid is (Type...
Consider the following region R and the vector field F a. Compute the two-dimensional curl of the vector field. b. Evaluate both integrals in the circulation form of Green's Theorem and check for consistency. c. State whether the vector field is conservative. F-3y,3x); R is the triangle with vertices (0, 0), (1, 0), and (0, 1) a. The two-dimensional curl is D (Type an exact answer, using π as needed.) b. Set up the integral over the region R. dy...
all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)