Evaluate the integrals in Exercises 29–32 (a) without using a trigono- metric substitution, (b) using a trigonometric substitution. y dy x dx V4 + x² 30. 29. V16 y2 x dx t dt 32. V4 – 1 31. 4 – x²

Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: Evaluate the integrals in Exercises 17–66. V3 – 2s ds 17. 18. ds V5s + 4 fovT 20. / 3y V7 – 3y² dy…

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Q: Compute the double integral R ye®Y dA where Ris the square -1 < x < 1, 0 < y< 2.

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Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. Use a comp cos(x) sin(y)…

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Q: Evaluate the integrals in Exercises using integration by parts

A: The integration given to us is  ∫tan-1ydy            (1)

Q: If F = (x + y, x² - y) a= y = √, calculate fr F.Tds by using computing the line integral directly.)

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Q: Exercise 10.6 Evaluate the line integral using a method of your choice. e¯*(cos y dx + sin y dy),…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $…

A: To evaluate the below line integral. ∮C5y2dx+3x2dy

Q: Evaluate the integrals in Exercises using integration by parts.

A: The integral given to us is  ∫y16-y2dy

Q: Evaluate the line integral by applying Green's theorem. 7xy dx + (x + y) dy, where C is the boundary…

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Q: Use the Fundamental Theorem of Line Integrals to calculate a F dr exactly, if F = 4x/3 i + ey/8 j,…

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Q: Evaluate the line integral Lav where C is given by the line y = lnx, 1 ≤ x ≤e. xy ds,

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Q: Evaluate the line integral by two methods: (a) directly and (b) using Green’s Theorem.3. ∮C xy dx +…

A: According to Greens theorem :

Q: Use Green's Theorem to compute the line integral | ry? dx – x² dy, -

A: Here we are going to use Greens theorem to find the line integral. Since, to compute the integral…

Q: Evaluate the integrals in Exercises 7. (x² + y² + z²) dz dy dx 0 J0

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Q: Use Green's theorem to find the line integral of 2x dx – 7x2 dy counterclockwise around the triangle…

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Q: Evaluate the integrals in Exercises 51–56 by making a substitution (possibly trigonometric) and then…

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Q: Evaluate the integrals in Exercises using integration by parts.

A: Integration of a function is the process of finding the anti-derivative of the function. The…

Q: Evaluate the integrals in Exercises 42–44. 42.∫21⟨tet, ln t , tan−1 t⟩dt43.∫2π0⟨sin t, cos t,…

A: Definition used -                ∫xexdx =ex(x-1)+c∫ln x dx = x(lnx-1)+c∫ tan-1x dx…

Q: Evaluate the integrals in Exercises  using integration by parts.

A: Note:- We’ll answer the 19th question since the exact one wasn’t specified. Please submit a new…

Q: Evaluate the line integral by the two following methods. dx + x2 dy Cis counterclockwise around the…

A: The solution is given in the next steps.

Q: Integrate f(z) = (7)° counterclockwise around the unit circle, using Cauchy's integral theorem if…

A: using cauchy residue theorem to find given integral...

Q: Use the property to estimate the best possible bounds of the integral. II. 5 sin“(x + y) dA, T is…

A: To estimate the best bounds of the integral.

Q: F(x) = sin(t) dt %3D 3x

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Q: Evaluate the integral in terms of u. sinh u• du = + C %3D 3.

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Q: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x =…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 5…

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Q: 2 dy dx (1 + x² + y²)² 18. -V1

A: Given integral is  ∫-11∫-1-x21-x22(1+x2+y2)dydx

Q: Evaluate the Iterated integral by converting to polar oordinates. .V 2x – x2 8V x2 + y2 dy dx

A: Given that  The double integral  To evaluate the integral by using polar coordinates

Q: Evaluate the integrals in Exercises 9 and 10. 9. 8x sin y de – 8y cos x dy C is the square cut from…

A: Explanation bye green's theoram in plane, we have  ∫∫R(∂N∂X-∂M∂Y)dxdy = ∮Mdx +Ndy compare the…

Q: sin 4zdz J 16+ sin ª 2= 4.

A: The given function is sin 4z16+sin4 2z We have to evaluate the integral of this function.

Q: Use Green's Theorem to evaluate the line integral below. dx + 5xy dy C: r = 1 + cos(0), 0 s0 s 2n

A: Consider the provided line integral ∫Cx2-y2dx+5xydy. Let M=x2-y2, and N=5xy. That implies,…

Q: Evaluate the line integral by the two following methods. dx + x2 Cis counterclockwise around the…

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

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Q: Use the residue theorem to calculate the contour integral |z|=5 dz. /zl=5 (z + 1)²(z + 2i)

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Q: Evaluate the triple integral z dV, where is E bounded by the paraboloid x= 4y+4z2 and the plane x=…

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Q: Integrate f(z) = counterclockwise around the unit circle, usin %3D 28 – 9.7 - Cauchy's integral…

A: Given function is fz=1z8-9.7 and the contour is the unit circle oriented counterclockwise.

Q: Q21 Verify Green's theorem for $. (xy² + x²)dx + (4x – 1)dy where Cis shown in the figure by (a)…

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Q: 8. Verify Green's Theorem for (6y – 3y? +x) dx + yx*dy where C is shown below by (a) computing the…

A: Given integral is ∮C6y-3y2+xdx+yx3dy Here C consists of two line,  C1:Line joining 0,0 and…

Q: Evaluate the triple integralE 7xdV, where E is bounded by the paraboloid x = 7y2 + 7z2 and the plane…

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Q: Evaluate the improper integrals in Exercises •3 dx 53. 54. In x dx V9 dy de (0 + 1)3/5 56. 55. (y –…

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Use symmetry to evaluate the double integral. x' dA, R = [-4, 4] × [0, 5]

A: Replace dA by dxdy x is from -4 to 4 y is from 0 to 5

Q: Use Green's Theorem to evaluate the line integral of F (x°, 9x)

A: Given, the line integral of F=x3, 9x around the boundary of the parallelogram in the following…

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate fo F·dR, where F(x, y) = (x²y² – 3x, r³y)…

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Q: Use a computer algebra system to evaluate the iterated integral. V 9 - y- y dz dx dy 9 - y

A: Consider the integral:…

Q: Use Green's Theorem to evaluate the line integral below. √ (x² − y²) dx + 7xy dy C:r = 1 + cos(8), 0…

A: Given integral is ∫Cx2-y2dx+7xy dy where C: r=1+cosθ,  0≤θ≤2π To Use: Green's Theorem to evaluate…

Q: Use a computer algebra system to evaluate the iterated integral. V1- y? y dz dx dy -V1- y

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Q: Evaluate the line integral using the Fundamental Theorem of Line Integrals. (3y dx + 3x dy), where C…

A: Given line integral is: I=∫c3ydx+3xdy It can be rewritten as: I=3∫cydx+xdy                ....(1) As…

Q: Evaluate the integrals in Exercises 9–12. 4 cos (x²) dx dy 2y 9. e dx dy y/2 10. 27 sin 7x² -dx dy…

A: Given: