Evaluate the double integral f(r, ) dA. 7/6 2 p2 sin(O) cos(O) dr do Jo Jo...
(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...
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
(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 -...
q2 please (1) Evaluate the integral (r-1) min(a, y) dy dr, Jo Jo where min(x, y) is the minimum value of r and y. (2) Let f,g : R → R be functions of one variable such that f" and g" are continuous. Show that (f"(x)-g"(y)) dydx = f(0) + g(0)-f(2)-9(2) + 2f'(2) + 2g'(0). o Jo (3) Let a > 0. In spherical coordinates, a surface is defined by r = 2acos φ for 0 φ 1. Find the...
1P Question 3 1 Evaluate the double integral: SS sin?(x) dx2 7 o (+ cos(2x)) 0} (x2 + cosº (x)) No answer text provided. 0}(– cos(2x)) 0} (x + 2 cos(2x)) NE Previous
Use polar coordinates to evaluate the double integral. Enter an exact form, do not use decimal approximation. SAS. 159e*?-, da, where R is the disk x2 + y2 = 64 nt
4-6 Sketch the solid represented by the double integral, and use your picture to evaluate the double integral. Do not compute the integral. 4. (5 - 2)dA, R= {(r,y) 0<x<5,0<y <3} R 5. sin ydA, R= [0,24] [0,2 6. II (4 – 2y) dA, R = [0, 1] x [0, 1]
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
all of tem (e) sin(30) + cos(20) do 1. Evaluate the indefinite integral. (a) [8x2 – 3x2 + 3+ – 2 dr (b) 1-1 + 7x – 34" da (e) [(3+ + 2)(+ – 2) dt (8) 223/2 - 3/3+ Fadz (n) 23" +22-1 de 2. Solve the initial value problem: g'(x) = 7.76 – 4.23 + 12: g(1) = 24 3. Solve the initial value problem: W'(t) = 6 sin(3t): h() = 6
(In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2) (In2)2 +1 -2 sin r+ (In 2)2 cos x Evaluate /2 cos z da In 2 2° cos x + 2° sin (In 2) ln 2 1 +ln2 ln2 (In 2)