find the line integrals along the given path C. ∫C (x - y) dx, where C: x = t, y = 2t + 1, for 0≤ t≤ 3

Q: Evaluate the double integral S S (11a°y³ + 11eš")dædy

A: We have to evaluate ∫36∫2611x3y8+11e5x dxdy   We evaluate this double integral using iterated…

Q: Find Particular integral (P.I) (D² -1)y =18

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Q: 2. Evaluate each of the following line integrals in two ways∗ . (a) Z C1 F~ 1 · d~r, where F~ 1(x,…

A: Given vector field is F→(x,y)=(2x-cosy)i^+(xsiny)j^F→.dr→=(2x-cosy)dx+(xsiny)dy C1 is the…

Q: The particular integral of (D – 1)y= x i,

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Q: Evaluate the integral. (e* i + 4t j + In(4t) k ) dt + C

A: The given integral is: ∫et i+4t3 j+ln(4t) k dt

Q: Evaluate the line integral Ĥ. dř where Ĥ = e" î + [xe" + In(2)] ĵ + º Â and the curve C is defined…

A: Given problem:-

Q: Evaluate the integral 2 ху S S xe dx dy 0 1

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Q: The improper integral A e B 0 C D) 1 + ∞ [** 0 e-x dx is

A: The given improper integral is: I=∫0+∞e-xdx

Q: Apply the composite Simpson's Rule with m = 1,2, and 4 panels to the integrals, and report the…

A: Since you have posted multiple questions but according to guidelines we will solve first question…

Q: Evaluate the line integral along the given path. S ² + y² + 2²) ds C: r(t) = sin(t)i + cos(t)j + 7k…

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Q: a) Evaluate the given integral In y TT In z dz dx dy 1 1 1

A: Finding the given integral

Q: Evaluate the integral S (t³ In ti + 3t³ sin (t*) j+ x-2 X(x+1) k) dt.

A: In this question, we have to find the integral of the given vector function. Here we integrate the…

Q: Which of the following integrals will yield In u+ C? A. SE B. S- x+1 D. S dx xdx C. S 2rdx = x+1 O…

A: From the following integrals will yield ln u+C Note:     Multiple questions are given, we are answer…

Q: E ralu ate the given ヤyle integral: S. x² rin dy dz dx

A: Given that, The integration is, ∫0π∫0x∫0xzx2siny dy dz dx We have to find the value of this…

Q: Evaluate each of the following line integrals. Sc [(x² - y2)dx + (2xz)dy + (xy-yz)dz] where C: x =…

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

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Q: Evaluate the integral, if it exists.

A: Given: ∫-π4π4t4 tant2+costdt

Q: 1. Evaluate the given line integral, I (-y,x – y) · dR, where C is the upper part of 4.x? + 9y? = 36…

A: we have to find the line integral  ∫C-y,x-y.dR→ where c is part of the ellipse 4x2+9y2=36 from…

Q: Compute each of the following line integrals. Cos(e=") ) dx + (x² + y+1) dy, where C is the circler…

A: Given integral is  ∫Cy-ecosex5!dx+x2+yy+1dyWhere C is the circle r=2.

Q: (b) Evaluate each of the following line integrals: (1) xds, where C is the portion of the curve x…

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Q: Evaluate the integral: S S. 4 dx dy 0 y? 294 3 196 3 392 3 98 3

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Q: Find Particular integral(P.I) (D'-1)y = 18

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Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: 2. Evaluate the following integrals. (a) Si S S*** xy dz dy dx

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Q: Evaluate the integral S xy dx dy

A: Explanation of the answer is as follows

Q: Evaluate the integral of (3x + 9y) dx dy, use the inner limits from 0 to y and outer limits from 0…

A: Given: The double integral ∫∫3x2+9y2dxdy, here the inner limits varies from 0 to y and outer limits…

Q: C * dt = 1 0.2t

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Q: 1 d.r. x² In(x) Consider the inmproper integral r10

A: The solution is in step 2

Q: Find the line integral along the given path C. f(x - y)dx, where C: x=t, y = 5t+7, for 0 st≤5 C √(x…

A: Topic:- application of integration

Q: 5. Evaluate the iterated integrals. a. b. [²³² (x+y)dx dy S S S xyz dx dy dz

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Q: 14. dy, where C: x = t, y = t², for 1 <t<2

A: Here, to evaluate: ∫Cxydy=∫12tt2(2t dt)=2∫12dt

Q: Find the line integral along the given path C. [(x - y)dx, where C: x=t, y = 3t+8, for 0 ≤t≤6 с √(x…

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Q: 3. Evaluate the following INDEFINTE integrals. (a) / (b) / va dy y dy (c) dy

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Evaluate the given line integral, |(-y,x – y) · dR, where C is the upper part of x² + y? = 4 from…

A: Given  ∫C(-y,x-y).dR→ where C is upper part of circle  x2+y2=4 from (-2,0) to (2,0).   Note-As per…

Q: Evaluate the line integral below over the path c(t) = (t², sin(#), e-3t+4) over the interval 0 < t <…

A: We have to evaluate the line integral.

Q: 1. Evaluate the following iterated integrals: (a) S x²y dxdy (b) Lx sin y dydx.

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Q: S( z +1) e2² dz

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Q: Given F = &lt; x2y, x &gt; and C is the line from (1,2) to (0,0Evaluate the integral (F•dr) by…

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Q: Find the integral | 5y In y dy. 5y In y dy = +C

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Q: Evaluate the following integrals. Show your complete solution. 2 dy 1. S Зу-4 2. S dv v+3

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Q: Find the line integral along the given path C. Ju- |(x- y)dx, where C: x = t, y = 5t + 6, for 0 sts2…

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Q: 5, find the line integrals along the given path C. In 13. | (x – y) dx, where C: x = 1, y = 21 + 1,…

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Q: over the graph y = e*, 0 < x < 1. Compute the path integral of f(x, y) = 2y² %D

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Q: Find the integral of t/(t^4+2) dt

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Q: Evaluate the following sum of iterated double integrals: 1 2y r2 r4-2y dz-a dx dy + Ax-a² dx dy e…

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Q: Compute the given double integrals a) L,dy ſ (x5 – y) dx

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

Q: A. Evaluate the following integrals: Sx² e**dx 1.

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Q: 15. Evaluate the integral ſo S, x²y² dy dx (a) directly, (b) integrating with respect to x first and…

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Q: 3. Find following integrals using method of substitution: Sze z dz a. 2 x2 b. S /1+x

A: Consider the provided integral, ∫ze-z22dz Find the expression for this integral using substitution.…

Q: Evaluate each of the following line integrals. x dy – y dx, 2n <t< 4TT (a) c(t) = (2 cos(t), 3…

A: According to the given information it is required to calculate the line integral. For part (1)