Find the line integral / (x² + y) í + y³ j ) • d7 where C consists of the three line segments from (7, 0, 0) to (7, 4, 0) to (0, 4, 0) to (0, 4, 9). Enter an exact answer. (? + y) 7 +y° 7 ). d7 = 87

Find the line integral / (x² + y) í + y³ j ) • d7 where C consists of the three line segments from (7, 0, 0) to (7, 4, 0) to (0, 4, 0) to (0, 4, 9). Enter an exact answer. (? + y) 7 +y° 7 ). d7 = 87

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Evaluate the integral |(2e' – 2x) dy +(2xy +1) dx using Green's theorem where C is C 64 ans:-- 3…

A: Using Greens theorem the integral over a closed path can be converted into a corresponding surface…

Q: If C is the line segment from (6, 1) to, (0,0), find the value of the line integral: S(5y i+ x) • dr…

Q: Evaluate the line integral -y dx + z dy + 2x dz, where C is the helix by 7(t) = (cos t, sin t, t),…

Q: Please solve the line integral Se F · dĩ In where: F = y²i+2r(y+1)j Is along 2 unique paths from the…

Q: 2. Find an upper bound of the absolute value of the integral e + 1 (a) dz, where C is the right half…

A: We know that : Imz=12z-zi . Therefore, ∫Cz2-Im(z)dz=∫02+2iz2-i2z-zdz.

Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: Use Green's Theorem to evaluate the line integral |(v - x)dx + (2x – v)dy for the given path. C: x =…

Q: fo F(1+ 2t, 1+ 3t)dt is equivalent to the line integral of F(x, y) on the line segment from (1,1) to…

A: Here we have to find is the given statement is true or false

Q: The integral ∫C[(3x2y+y2)dx+(x3+2xy)dy] is independent of the path. Evaluate the integral where C is…

A: Given: R=ti+(t2+t-2)j for 0<=t<=2

Q: Compute the line integral Sc 2.xy dx + x² dy along the following curves. (a) C1 along the circle x2…

A: In given question that is a conservative vector field mean exact integration in which intrgration…

Q: Evaluate the line integral xyz ds where C is the line segment joining the points (1, – 1, 1) to (1,…

Q: 3. Set up the integral to find fSfr r dV where T is the tetrahedron in the first octant under the…

Q: The line integral g-dr where g= (2ry - y³)i + (a² – 2ry)j and r(t) = cos ti + sin tj,0<t<a has a…

A: Use green theorem.

Q: 4. Evaluate the integral f. x'y°dy – x°y'dx, where C is the square determined by the lines x = 0, y…

A: As per Bartleby's answering policy, we can answer only one question and here we have answered the…

Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

Q: Evaluate the line integral along the curve C. (xz + y) ds, C is the curve r(t) = (-4 - t) i + 2t j -…

Q: Assuming that C is the counterclockwise oriented boundary curve of the unit square in the first…

A: It is an simple and easy question on vector calculus Can be easily solve by use of green's theorem

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

Q: (2) Use the transformaiton u = xy, v = x² – y? to find JJ (æ* – y*)e*³ dA where R is the region in…

A: Given: The region bounded by the hyperbola xy=1 &3, x2-y2=3 &4 Where u=xy and v=x2-y2

Q: Given F = (2xze*²z – 4, cos z, x²e*z – 3ycos?z sin z) 1. You are to show that the line integral S.…

Q: Evaluate the line integral [39a²³yzds with respect to s along the 2 curve C: x = t, y t, y = t²,₁…

Q: Evaluate the line integral ,F. dr where F = (sin x, –2 cos y, 5xz) and C is the path given %3D by…

A: Integral F.dr = integral F(r(t)).r'(t) dt

Q: 1. Evaluate the line integral f(z, y) ds where f(x, y) = Vx+ 2y and C is the straight-line segment…

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x – y)dy for the given path. C: x =…

Q: Evaluate the line integral S, xy dx + x² dy, where C is given by y = x³,1 < x < 2. ху A 31 B 124 33…

Q: Given that F = (4y² +e") ï+ (xe" +8xy) j, calculate the line integral So F • dr exactly, where C is…

Q: Evaluate the line integral along the given paths. y?) ds + (a) C: line segment from (0, 0) to (8,…

Q: 2. Evaluate the given line integral, (-y,x – y) · dR, where C is the line segment from (1,0) to…

Q: - Evaluate the integral 4-z²-y² 1 dz dy dx Jo 4-z²-y² x² + y² + 2² using spherical coordinates.

A: To evaluate ∫-22∫04-x2∫-4-x2-y24-x2-y2 1x2+y2+z2 dzdydx

Q: Question 3. Compute the integral - dz 8+z where y is the rectangle with vertices +3+ i with the…

Q: 1. Evaluate the line integral of E = xax - y ay along the segment P₁ to P2 of the circular path as…

Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 || | (r²sin²0 +z²) dz r dr d0 0 0 -1/2

Q: Evaluate the line integral T, (“+y) dx + 4 ry dy where L is the path, -> r) = (3 t, 2) with 0 <t <1.…

A: We evaluate given integral

Q: 1. Evaluate the given line integral, | (2² – y,y) · dŘ, where C is the part of a = y? – 1 from (0,…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: If C is the line segment from (1, 5) to, (0,0), find the value of the line integral: So(4y? i + 4x…

Q: Evaluate the line integral di the path over C from to Q(2,4) P(O,) where F(xy) 2xy°2+3y5 13D to ネソーメ…

Q: Evaluate the line integral Sa y dx +z dy, where C is the line segment from (4) (-1, 1, 2) to (2,3,…

Q: Use Green's Theorem to evaluate the line integral (y - x)dx + (2x - y)dy for the given path. C: x =…

Q: 14. Find the line integral of f(x, y, z) = V3/(x² + y² + z?) over the curve r(t) = ti + tj + tk, 1 <…

Q: 3 2 Use a line integral to calculate the length of the helix ř(t) = (a cost, a sint, bt) 0<t < 2n…

Q: Use the Fundamental Theorem of Line Integrals to find the exact value of the path-independent line…

A: First of all hare we check for the path independent line integral then solve for moving over the…

Q: Evaluate the line integral 9x²yzds with respect to s along the 2 curve C: x=t, y = t², z = t³(0 ≤ t…

A: Given: ∫C9x2yzds x=t y=t2 z=23t3 0≤t≤1 To find: Value of the given integral.

Q: Q.01: Use Green's theorem to evaluate the line integral £ e2*sin2ydx + (e²*cos2y)dy, where C is the…

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? +…

A: The given line integral is, I=∮y4x2+y2dx+x2x2+3y2dy We know the Green's theorem:…

Q: Find the line integral of F(x, y, z) = x'i + yj+ zk along the line segment C from the origin to the…

Q: 3. Set up the integral to find fffr x dV where T is the tetrahedron in the first octant under the…

A: To set up the integral to find ∭TxdV

Q: Calculate the value of the line integral fds where f(x,y,z)=e² and C is described by C (x, y,…

Question

X Incorrect.
Find the line integral
/ (2 + y) í +y° j )•d7 where C consists of the three line segments from (7, 0, 0) to (7, 4, 0) to
(0, 4, 0) to (0, 4, 9).
Enter an exact answer.
+ y) í +y³
7)dア
87

Expert Solution

Step 1

The given line integral is $\int_{C} ((x^{2} + y) \vec{i} + y^{3} \vec{j}) \cdot d \vec{r}$ where C is the line segment from $(7, 0, 0)$ to $(7, 4, 0)$ to $(0, 4, 0)$ to $(0, 4, 9)$