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4. (10 points, 5 points each) Multiple choice: i. Which one of the following integrals is...
please respond with explanations for each step. thank you Problem 4 Evaluate the line integrals (a) (10 points) y da...
please respond with explanations for each step. thank
you
Problem 4 Evaluate the line integrals (a) (10 points) y da 2ax dy, where C is the curve r(t) (2t + 1) i+ 3t2 j, 0t 1. (b) (10 points) (ryz) ds, where C is the line segment from the point (2, 1,0) to the point (4,3,6) (c) (10 points) F.dr,where F is the vector field F(x, y) = yi - rj and C is the curve given by r(t) t2i+...
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral...
Please Answer the Following Questions (SHOW ALL WORK)
1.
2.
3.
4.
Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the c...
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr-
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Evaluate...
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Evaluate the integral. 5 In 5 1) S. ey dx dy el B) 4 A) 8 D) 9 C) 18 Integrate the function f over the given region. 2) f(x, y)- over the trapezoidal region bounded by the x-axis, y-axis, line x -5, and line 9 D) 60 A) 25 B) 40 C) 30 Write an equivalent double integral with the order of integration reversed....
U Question 15 "C 7 pts "С If S is the surface of the cylinder E=...
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
Use triple integrals to find the volume of the solid E bounded by the parabolic cylinder...
Use triple integrals to find the volume of the solid E bounded by the parabolic cylinder z=1 - y2 over the square (-1, 1] x [-1, 1) in the xy-plane. Hint: Volume(E) = SSSE 1 DV Answer: 8 3 z=1 - 22 In each of the given orders, SET UP the integrals for a function f over the solid shown. If this can not be done using a single set of triple integrals, state NOT POSSIBLE. a) dx dy dz...
+ -/15 points scacats 15.6.033. The figure shows the region of integration for the integral. ["lib.*rex,...
+ -/15 points scacats 15.6.033. The figure shows the region of integration for the integral. ["lib.*rex, y, z) oz oy ok f(x, , z) dz dy dx Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume y(x) = x and z(y) = 9 - y.) ;Y, 2) dz dx dy Y, 2) dx dy dz R(x, y, z) dx dz dy f(x, y, z) dy dx dz F(x, y, z) dy dz dx
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2)...
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
calculus 3. Answer all of the following, I will rate your work if you do so....
calculus 3.
Answer all of the following, I will rate your work if you do
so.
Evaluate the double integral || xy2da, where Ris the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. Evaluate the iterated integral. 1 ya x-y xy dz dx dy xy dz dx dy 0 V The figure below shows the solid region Ein the first octant bounded by the...
please respond with explanations for each step. thank
you
Problem 4 Evaluate the line integrals (a) (10 points) y da 2ax dy, where C is the curve r(t) (2t + 1) i+ 3t2 j, 0t 1. (b) (10 points) (ryz) ds, where C is the line segment from the point (2, 1,0) to the point (4,3,6) (c) (10 points) F.dr,where F is the vector field F(x, y) = yi - rj and C is the curve given by r(t) t2i+...
Please Answer the Following Questions (SHOW ALL WORK)
1.
2.
3.
4.
Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) - (sin t, cos t, sin 2t), 0 s t s 27. (Hint: Observe that C lies on the surface z - 2xy.) F dr-
6. -1.25 points My Notes Evaluate (y 3 sin x) dx + (z2 +7 cos y) dy x3 dz COS JC where C is the curve r(t) -...
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Evaluate the integral. 5 In 5 1) S. ey dx dy el B) 4 A) 8 D) 9 C) 18 Integrate the function f over the given region. 2) f(x, y)- over the trapezoidal region bounded by the x-axis, y-axis, line x -5, and line 9 D) 60 A) 25 B) 40 C) 30 Write an equivalent double integral with the order of integration reversed....
U Question 15 "C 7 pts "С If S is the surface of the cylinder E= {(x,y,z) : 32 + y < 4,1523}, oriented outwards, which of the following (after applying the Divergence Theorem) will compute zyz) - dS? 40 O (1 + y2 cos & sin 6)r dr de dz REC O 1988 6%" /*(1 + == sin ®)r dr do dz %%% %%% %%% (r cos 0 + 32 + y2 z cos ( sin 0), dr do...
Use triple integrals to find the volume of the solid E bounded by the parabolic cylinder z=1 - y2 over the square (-1, 1] x [-1, 1) in the xy-plane. Hint: Volume(E) = SSSE 1 DV Answer: 8 3 z=1 - 22 In each of the given orders, SET UP the integrals for a function f over the solid shown. If this can not be done using a single set of triple integrals, state NOT POSSIBLE. a) dx dy dz...
+ -/15 points scacats 15.6.033. The figure shows the region of integration for the integral. ["lib.*rex, y, z) oz oy ok f(x, , z) dz dy dx Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume y(x) = x and z(y) = 9 - y.) ;Y, 2) dz dx dy Y, 2) dx dy dz R(x, y, z) dx dz dy f(x, y, z) dy dx dz F(x, y, z) dy dz dx
Evaluate the following integrals (from A to E) A. Integration by parts i) ſ (3+ ++2) sin(2t) dt ii) Z dz un (ricos x?cos 4x dx wja iv) (2 + 5x)eš dr. B. Involving Trigonometric functions 271 п i) | sin? ({x)cos*(xx) dx ii) Sco -> (=w) sins (įw) iii) sec iv) ſ tan” (63)sec^® (6x) dx . sec" (3y)tan?(3y)dy C. Involving Partial fractions 4 z? + 2z + 3 1) $77 dx 10 S2-6922+4) dz x2 + 5x -...
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t
(1)...
calculus 3.
Answer all of the following, I will rate your work if you do
so.
Evaluate the double integral || xy2da, where Ris the region in the first quadrant enclosed by the circle x2 + y2 = 4 and the lines x = 0 and y = x. Evaluate the iterated integral. 1 ya x-y xy dz dx dy xy dz dx dy 0 V The figure below shows the solid region Ein the first octant bounded by the...
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