Q3) Calculate the following integrals over the given C curves by using the Cauchy integral formula. dz C: |zi| 1 circle a) - (2²+7²) z3 (z+2)²(z-1) b) - -dz C: |zi| 3 circle

Q: The length of the curve y = 3 - 4Vx for 0 < x < 3 is calculated by the integral: %3D Select one: 3 O…

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Q: Let C be the line segment from the origin to the point (2, 3). [(y² + xj). dr

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Q: 12. Find the area of the region enclosed between the curves defined by the equations y = √(x + 2), y…

A: We have to evaluate the area of the region bounded by the curve y=x+2 and the line y=x using the…

Q: hat is the area of the region bounded by the line x = 4 and the curve x³ = x² + 2xy - y² = 0. ht:…

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Q: 2x4 1+x² a) [: dx b) [ cos² cos² 2x dr

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Q: Find the value of "k" for which the line integral 1+ky? 1+ kx? dy taken č [a+ xy)? (1+xy)? (1+ xy)?…

A: We will find out the required value.

Q: [[(2x + y²) da + 2xy dy], where C is the line segment from (-1,0) to (1, 2) Evaluate in two…

A: The line integral ∫CMdx+Ndy involves the integration over a specific path. In this case, the line…

Q: Evaluate the contour integral z²dz along the following curves. (a) C₁: the line segment from -i to…

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Q: f(2) = z? +E Evaluate the integral of f(2) along the following curves: a. a is a straight line…

A: The given problem is related with complex integration. Given that fz = z2 + z¯ . We have to evaluate…

Q: Find : ( 39 - Sincm) dx +(2x*) dy when C is the boundary of the limited area by curvess y= e* and in…

A: Given that I=∫c3y-sin x dx+2x2 dy                                   ……(1)   Boundary is given as…

Q: = Jó 7xds where C consists of the arc C₁ of the parabola y 3x² from (0,0) to Compute the integral I…

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Q: -dz Q5/ (A) Find the value of the integral 3 where C is the circle z+2 = z(z+1)"*1

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Q: where y is the circle {|z – 2| = 1} with counter clockwise orientation. (b) cos(2) -dz, 22 + 2iz – 1…

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Q: Evaluate one the integrals: 2x-1 8 a) ! -dx 2 X x² + 3x + 1

A: Introduction: Integration is the calculation of an integral. Integrals in mathematics are used to…

Q: Q6. A: Evaluate the integrals: sec x dx dx 2) L, | VIn(secx+ tan x) -2 (4+x²)3/2

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Q: 3) Find the area of the surface formed by revolving the graph f(x) = ;x³ about the x-axis over the…

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Q: A) Give f(x)-V-3 find f-*(x) ,x >0 B) : Find the area bounded by the curve y = f(x) =v2x +1 and the…

A: We have to find  A) f-1(x) for f(x) =√(x-3)  B) area bounded by the curve y = √(2x+1) and the lines…

Q: (x² + y²)dx + 2xydy where C It's the curve y = x³ from x = 0 to x = 1

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Q: Using contour integrals to compute the following integrals So +1 (a) fo° (42dx, (b) √²+2x+2dx, (c)…

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Q: Find the arclength of y = 4x² - 2 on 0 ≤ ≤ 2

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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…