22 Calculate the value of the integral over the following C curves. a) C:l2+1| = 1 1, %3D c) C:l오+1 = 1.4 %3D d) c12+5-511-구 %3D cou

Q: 4) Compute the integral where is the closed chrve SRe (z²)dz -2

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Q: 17. Evaluate the line integral xezds, where C is the line segment from (0,0,0) to (1, 2, 3).

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Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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A: C consist line from A (2, 0, 1) to B(3, 3, 1) Now,

Q: Show that the following line integral is path independer (3,5) y² %3D cosh( )(10xdx +6ydy) (0,0) 3

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Q: Calculate the double integral of f(x, y) over the triangle indicated in the following figure: 4- 3.…

A: Given:

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Q: Evaluate the line integral x'z ds, where C is the line segment from (0, 5, 2) to (4, 6, 5).

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Q: 2. Sketch the region of integration of the given integral Q in #1. Set up Q by reversing its order…

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Q: Apply Green's Theorem to evaluate the integral P (3y2 dx + 3x2 dy), where C is the triangle bounded…

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Q: Evaluate the line integral of x^3(z)ds, where C is the line segment from (0,8,2) to (7,4,6).

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Q: 8. What domain D in space minimizes the value of the integral // (4x² + y^ + z2² – 4)dV

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Q: Compute the integral of f(x) = 0.4 – 2x² + 40x5 from a = 0 to b = 0.8 using i. Trapezoidal Rule with…

A: Numerical integration

Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Evaluate the line integral, where C is the given curve.  ∫(with c in subscript) (x + yz) dx + 2x…

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Q: 5) Set the iterated double integral ļ) dydx メモービ テ as Jady up

A: Please see the below explanation.

Q: 2. Set up an integral to find the exact length of the curve defined by 1 f(r) 1 In r %3D where 1<r <…

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Q: Evaluate the line integral ∫Cydx+xdy along the curve y=x2 from the point O(0,0) to the point A(1,1)…

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Q: Evaluate the double integral. [[ ×20 (2+2y) dA, D is bounded by y = x, y = 2³₁x20

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Q: Evaluate the double integral.18. , D is bounded by y = x, y = x3, x ≥ 0

A: To evaluate the double integral. Given that  D is bounded by y = x, y = x3, x ≥ 0. We can define…

Q: Show that the following line integral is path independent (3,2) cosh (0,0) (8xdx+6ydy) 4.

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Q: 3) Show that the line integral is independent of path and then evaluate the inte S, sin y dx + (x…

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Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: 5. Apply the Composite Midpoint Rule with m 1,2, and 4 panels to approximate the integrals. Compute…

A: Concepts introduction: Mid point rule Assume that, the function fx is continuous on a,b and m be a…

Q: 2. Compute the line integral of f(r, y) = r over the curve C, where C is a triangle formed by…

A: Now we have to find the line integral: ∫C x dswhere C is triangle joining the points:  (0, 0),  (1,…

Q: Show that the following line integral is path independent and evaluate its value. Show the details…

A: Step:-1 Note:- 1. ∫∇F.dr =∫fx i +fy j dx i +dy j  2. Fundamental Theorem of Calculus:- ∫bc F'(x) dx…

Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Consider the integral 2 6z² In(z) dz

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Q: The improper integral fx dx is

A: An improper integral is the limit of a definite integral as an endpoint of the interval of…

Q: Evaluate the integral. 4 2t 9 -i- j+¬Vt k dt (9+?)*

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Q: Use the the tabulated values of the integrand to estimate the integral with Trapezoidal Rule with…

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Q: I need help understanding/ solving attached question for CALC.

A: Given the two parametric form of the line segment from (3,0,1) to (1,4, -2).

Q: 3. Consider the line segment L = [-1-i, 1 + i]. Calculate the value of the integral 1₁² z² dz.…

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Q: Evaluate the integral fff, xyzdV,where: E = {(x, y, z)|–1 <x< 1,0< ys 2,1 szs 2}

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Q: Evaluate by Cauchy’s integral formula: ∫ c e3z/(z+2)4dz where c: mode z = 4.

A: To find - Evaluate by Cauchy's Integral formula : ∫Ce3zz + 24 dz where C : z = 4     Formula used -…

Q: Show that the following line integral is path independent an (3, 2) S cosh(+ X (0,0) (8xdx+6ydy)

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Q: Compute the line integral of F = (-y, x) along the line segment from (0,0) to (1,1).

A: The line integral is evaluated using the following formula  ∫cF→x,yds=∫abF→rtr'tdt    , a≤t≤b   ,…

Q: 10.Calculate the double integral ffRXsinydydx, where R is bounded by y=0, y=x2, x=1.

A: Fubini's Theorem- If f(x, y) is continuous over the region R defined by a≤x≤b,   c≤y≤d then,…

Q: 2. Use Cauchy3 Integral formula, Evaluate the following • I=0 e %3D

A: The given problem is to evaluate the given complex integral over the given contour using cauchy…

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Q: 3, Let R be the of: y: sinx region endlosed bu the grophs n enclosed by and 1 x70 . Groph R and…

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Q: Evaluate the integral: (In z)6 dz %3D

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Q: 22 Calculate the value of the integral over the following C curves, a) C:|2+1| = 1

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the line integral of C in two ways; A) Directly. B) Using Green's theorem. C eata formed by the…

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Q: dl /x² + y² + 4

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Q: Evaluate the triple integral [[Scosys3 12xy²z³ dV_over the rectangular box G define by the in…

A: We have to find value of given triple Integral.