1.109. {a) If A (4zy-3x2z2)i+ (4y + 2x2)j + (1-2x z)k, prove that A dr is independent of the curve C joining two given points. (b) Evaluate the integral in (a) if C is the curve from the points (1,-1, 1) to (2, -2, -1). Ans. (b) -19

Q: AIS. 4. Compute the area of the surface formed when f(r) = 2 + cosh(r) between 0 and i is rotated…

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

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A: Given :∫12∫1x∫y2lnyz dz dy dx=I

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A: Green's Theorem, ∫CPdx+Qdy=∬D∂Q∂x-∂P∂ydA Compare ∫CPdx+Qdy=∫Cyexdx+2exdy Implies that, P=yex, Q =…

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A: Given

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A: Given : ∫1+∞dxx  in which 1x6+1≥1x

Q: Compute the line integral of f(x)=2x over the curve y=x² from (0,0) to (1,1). |

A: The line integral of f(x)=2x over the curve y=x2 from (0,0) to (1,1)

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A: Given query is to find the the line integral for the y = 2x over y = x2.

Q: 2. Evaluate. the fallowing.integrals.a.fter.seveoiag.the areler.of.integratiam. dydx Ans..In)/4 C.…

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Q: 7. Find the Lebesgue integral over [0, 2] for the following function. f(x) = { , EQ 3z +2, IEI %3D

A: Given  f(x)=x2        x∈Q3x+2  x∈I

Q: S. 09. (a) If A = (4xy-3x2z")i + (4y + 2x")j + (1 2x%z)k, prove that A• dr is independent of the…

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Q: 15 Evaluate the improper integral J. (x- dx

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A: Solution is given below:

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Q: consider the following integrals: dt ·00 a+cost dt where a > 2, 00 dt i). ini Mark the correct one…

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

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Q: 15. 91? – 6t +5 dt 16. Find the area under the curve for y = 3x² over the interval [2,5].

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

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Q: 1. Express the integral S S f(x,y, z) dzdxdy as an iterated integral in the other five different…

A: I1=∫02∫0y3∫0y2f(x,y,z) dz dx dy0≤y≤20≤x≤y30≤z≤y2I2=∫08∫0x3∫0y2f(x,y,z) dz dy dxx=y3,y=x30≤y≤x3y=0…

Q: 6. Compute the following integrals using Residue Theorem. 5z - 2 b. dz a. √21-23 = dz · Soz (²-2) 4…

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Q: 5, set up the appropriate iterated integrals in rios for I f dV on the indicated domains.

A: Step:-1 Given that  The equation of tetrahedron is z = 4 -2x -y⇒2x + y+z =4 ---(1) so, bounds or…

Q: 2. We have seen that the FTC for line integrals implies fc Vf - dĩ = 0 for any smooth closed path C…

A: FTC for line integrals implies ∫C∇f·dr→=0 for any smooth closed path C and any smooth function f (a)…

Q: (B) Compute div F and curl F for F= x²yi- (z3-3x)j + 4y2k %3D

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.