5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.) 5. (15 points) Consider 3 dz r dr d, 20. a. Convert the integral to rectangular coordinates with the order d: dr dy (but don't evaluate.) b. Convert the integral to spherical coordinates (but don't evaluate.)
Evaluate the line integral - dr by evaluating the surface integral in Stokes Theorem with an appropriate choice of metal Close counterdeckwite orientation when viewed from above С F-6²-82-x².7² -2²) C is the boundary of the square Ix 13. lys 13 in the plane 2 #0 Rewrite the given in integral as a | as a surface integral fro-SSO ds C 5 Evaluate the integral $r..-Type an exact answer
(a) Use the obvious identity i-re-u to evaluate the integral sin dr. (b) Use the double angle formula and integrate by parts to evaluate the integral in da (c) Prove that both of these integrals converge as improper Riemann integrals (albeit for different reasons). (d) Use scaling to evaluate the integral r.sinatz dr dar for tE R. (a) Use the obvious identity i-re-u to evaluate the integral sin dr. (b) Use the double angle formula and integrate by parts to...
Evaluate the line integral ∫ F *dr where C is given by the vector function r(t). F(x, y, z) = (x + y2) i + xz j + (y + z) k, r(t) = t2i + t3j − 2t k, 0 ≤ t ≤ 2
072 5+292 Evaluate the cylindrical coordinate integral dz r dr do The value is 960 (Type an exact answer, using s as needed.)
Evaluate the following integral in cylindrical coordinates. z T 4 4 dz r dr de 00-4 -4 4 T 4 4 SSS dz r dr do = (Type an exact answer, using a as needed.) 00-4
Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution: Problem 4 A definite integral I is given as .b I=| f(x) dr a=0 b=2 f(x) = e-r' ; ; ; Evaluate the integral using the three-point Gaussian quadrature method Solution:
5. Evaluate the integral sec" x dr. 6. Evaluate the integral I 2 dx X3 V x2 – 1 >1. 7. Evaluate the integral dc I VAI 8. Evaluate the integral 19 - 22 dc. .x2
f(x)dx=_, | f(r)dr? Given that what IS Preview answer Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1-5, A2-4, A3-2 and A4:1 y-fx) A1 АЗ A2 igure is NOT to scale Enter your answer as a whole number Evaluate dx. 1 + e1.82z 71.7 answer If -16 f(x)dx = 12 and r-16 g(x)dx = 15 J- 85 and -16 h(z)dz 21 -85 what does the following integral...
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...